{"id":5045,"date":"2023-03-25T05:26:46","date_gmt":"2023-03-25T05:26:46","guid":{"rendered":"https:\/\/theexampillar.com\/ncert\/?p=5045"},"modified":"2023-03-28T06:15:59","modified_gmt":"2023-03-28T06:15:59","slug":"ncert-solutions-class-9-science-chapter-10-gravitation","status":"publish","type":"post","link":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-science-chapter-10-gravitation\/","title":{"rendered":"NCERT Solutions Class 9 Science Chapter 10 Gravitation"},"content":{"rendered":"<h2 style=\"text-align: center;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">NCERT Solutions Class 9 Science\u00a0<\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">The NCERT Solutions in English Language for Class 9 Science <strong>Chapter &#8211; 10 (Gravitation) <\/strong>has been provided here to help the students in solving the questions from this exercise.\u00a0<\/span><\/p>\n<h2 style=\"text-align: center;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Chapter &#8211; 10 (Gravitation)\u00a0<\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif; color: #ff0000;\"><strong>Questions<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\"><strong>1. State the universal law of gravitation.<br \/>\n<\/strong><strong>Answer &#8211; <\/strong>Every object in the universe attracts every other object with a force which is proportional to the product of their masses and inversely proportional to the square of the distance between them. The force is along the line joining the centres of two objects.<\/span><br \/>\n<span style=\"font-family: georgia, palatino, serif; color: #000000;\">F \u221d <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{Mm}{d^2}\" alt=\"\\frac{Mm}{d^2}\" align=\"absmiddle\" \/>\u00a0or F = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{GMm}{d^2}\" alt=\"\\frac{GMm}{d^2}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\"><strong>2.<\/strong>\u00a0<strong>Write the formula to find the magnitude of the gravitational force between the earth and an object on the surface of the earth.<br \/>\n<\/strong><strong>Answer &#8211;\u00a0<\/strong>Let M<sub>E<\/sub>\u00a0be the mass of the Earth and m be the mass of an object on its surface. If R is the radius of the Earth, then according to the universal law of gravitation, the gravitational force (F) acting between the Earth and the object is given by the relation:<br \/>\n<span id=\"MathJax-Element-1-Frame\" class=\"mjx-chtml MathJax_CHTML\" style=\"box-sizing: border-box; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: 400; font-size: 18.08px; letter-spacing: normal; overflow-wrap: normal; word-spacing: 0px; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; font-variant-ligatures: normal; font-variant-caps: normal; orphans: 2; widows: 2; -webkit-text-stroke-width: 0px; background-color: #ffffff; position: relative;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mi&gt;F&lt;\/mi&gt;&lt;mo&gt;=&lt;\/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;G&lt;\/mi&gt;&lt;msub&gt;&lt;mi&gt;m&lt;\/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mn&gt;1&lt;\/mn&gt;&lt;\/mrow&gt;&lt;\/msub&gt;&lt;msub&gt;&lt;mi&gt;m&lt;\/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mn&gt;2&lt;\/mn&gt;&lt;\/mrow&gt;&lt;\/msub&gt;&lt;\/mrow&gt;&lt;msup&gt;&lt;mi&gt;r&lt;\/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mn&gt;2&lt;\/mn&gt;&lt;\/mrow&gt;&lt;\/msup&gt;&lt;\/mfrac&gt;&lt;\/math&gt;\"><span id=\"MJXc-Node-1\" class=\"mjx-math\" aria-hidden=\"true\"><span id=\"MJXc-Node-2\" class=\"mjx-mrow\"><span id=\"MJXc-Node-3\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\">F <\/span><\/span><span id=\"MJXc-Node-4\" class=\"mjx-mo MJXc-space3\"><span class=\"mjx-char MJXc-TeX-main-R\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{Gm_1m_2}{r^2}\" alt=\"\\frac{Gm_1m_2}{r^2}\" align=\"absmiddle\" \/><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000; font-family: georgia, palatino, serif;\"><strong>Questions <\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\"><strong>1. What do you mean by free fall?<br \/>\n<\/strong><strong>Answer &#8211;\u00a0<\/strong>Whenever an object falls toward earth under the force of gravity one and no other force is present, the motion of object is said to be \u201cfree fall\u201d.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\"><strong>2. What do you mean by acceleration due to gravity?<br \/>\n<\/strong><strong>Answer &#8211;\u00a0<\/strong>The acceleration of free fall is the acceleration due to gravity. We can also say the acceleration of an object due to gravitational force of earth acting on it is known as acceleration due to gravity.<br \/>\nThe value of the acceleration due to gravity on Earth is, g = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{9.8m}{s^2}\" alt=\"\\frac{9.8m}{s^2}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000; font-family: georgia, palatino, serif;\"><strong>Questions <\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\"><strong>1. What are the differences between the mass of an object and its weight?<br \/>\n<\/strong><strong>Answer &#8211;\u00a0<\/strong>The differences between the mass of an object and its weight are tabulated below.<\/span><\/p>\n<div class=\"table-responsive\" style=\"text-align: justify;\">\n<table class=\"table table-bordered\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\"><strong>Mass<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\"><strong>Weight<\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Mass is the quantity of matter contained in the body.<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Weight is the force of gravity acting on the body.<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">It is the measure of inertia of the body.<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">It is the measure of gravity.<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">It only has magnitude.<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">It has magnitude as well as direction.<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Mass is a constant quantity.<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Weight is not a constant quantity. It is different at different places.<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Its SI unit is kilogram (kg).<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Its SI unit is the same as the SI unit of force, i.e., Newton (N).<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\"><strong>2. Why is the weight of an object on the moon 1\/6th its weight on the earth?<br \/>\n<\/strong><strong>Answer &#8211;\u00a0<\/strong>The mass of moon is 1\/100 times and its radius 1\/4 times that of earth. As a result, the gravitional attraction on the moon is about one sixth when compared to earth. Hence, the the weight of an object on the moon 1\/6th its weight on the earth.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000; font-family: georgia, palatino, serif;\"><strong>Questions <\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\"><strong>1.<\/strong>\u00a0<strong>Why is it difficult to hold a school bag having a strap made of a thin and strong string?<br \/>\n<\/strong><strong>Answer &#8211;\u00a0<\/strong>We know that lesser is the surface area of an object the more is the pressure it exerts. Hence, it is difficult to hold a school bag having a strap made of thin and strong string, because the thin string has very less contacting area in case of a school bag having a strap made of thin and strong string which increases pressure which is un comfortable to carry the school bag.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\"><strong>2. What do you mean by buoyancy?<br \/>\n<\/strong><strong>Answer &#8211;\u00a0<\/strong>The upward force possessed by a liquid on an object that\u2019s immersed in it is referred to as buoyancy.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\"><strong>3. Why does an object float or sink when placed on the surface of water?<br \/>\n<\/strong><strong>Answer &#8211;\u00a0<\/strong>An object floats or sinks when placed on the surface of water because of two reasons.<br \/>\n<strong>(i)<\/strong> If its density is greater than that of water, an object sinks in water.<br \/>\n<strong>(ii)<\/strong> If its density is less than that of water, an object floats in water.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000; font-family: georgia, palatino, serif;\"><strong>Questions <\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\"><strong>1. You find your mass to be 42 kg on a weighing machine. Is your mass more or less than 42 kg?<br \/>\n<\/strong><strong>Answer &#8211;\u00a0<\/strong>When you weigh your body, an upward force acts on it. This upward force is the buoyant force. As a result, the body gets pushed slightly upwards, causing the weighing machine to show a reading less than the actual value.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\"><strong>2. You have a bag of cotton and an iron bar, each indicating a mass of 100 kg when measured on a weighing machine. In reality, one is heavier than other. Can you say which one is heavier and why?<br \/>\n<\/strong><strong>Answer<\/strong> -The cotton bag is heavier than the iron bar. The cotton bag experiences larger up thrust of air than the iron bar. So, the weighing machine indicates a smaller mass for cotton bag than its actual mass.<\/span><\/p>\n<p style=\"text-align: center;\"><span style=\"text-decoration: underline; color: #ff0000;\"><span style=\"font-family: georgia, palatino, serif; font-size: 14pt;\"><strong><b>Excercises<\/b><\/strong><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\"><strong>1.<\/strong>\u00a0<strong>How does the force of gravitation between two objects change when the distance between them is reduced to half?<br \/>\n<\/strong><strong>Answer &#8211;\u00a0 <\/strong>Consider the Universal law of gravitation,<br \/>\nAccording to that law, the force of attraction between two bodies is<br \/>\nF = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{(Gm_1m_2)}{r^2}\" alt=\"\\frac{(Gm_1m_2)}{r^2}\" align=\"absmiddle\" \/><br \/>\nWhere,<br \/>\nm<sub>1<\/sub>\u00a0and m<sub>2<\/sub> are the masses of the two bodies.<br \/>\nG is the gravitational constant.<br \/>\nr is the distance between the two bodies.<br \/>\nGiven that the distance is reduced to half then,<br \/>\nr = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{2}r\" alt=\"\\frac{1}{2}r\" align=\"absmiddle\" \/><br \/>\nTherefore,<br \/>\nF = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{(Gm_1m_2)}{r^2}\" alt=\"\\frac{(Gm_1m_2)}{r^2}\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"font-family: georgia, palatino, serif; color: #000000;\">F = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{(Gm_1m_2)}{\\left&amp;space;(\\frac{r&amp;space;}{2}\\right&amp;space;)^2}\" alt=\"\\frac{(Gm_1m_2)}{\\left (\\frac{r }{2}\\right )^2}\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"font-family: georgia, palatino, serif; color: #000000;\">F = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{(4Gm_1m_2)}{r^2}\" alt=\"\\frac{(4Gm_1m_2)}{r^2}\" align=\"absmiddle\" \/><\/span><br \/>\n<span style=\"font-family: georgia, palatino, serif; color: #000000;\">F = 4F<br \/>\nTherefore once the space between the objects is reduced to half, then the force of gravitation will increase by fourfold the first force.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\"><strong>2. Gravitational force acts on all objects in proportion to their masses. Why then does a heavy object not fall faster than a light object?<br \/>\n<\/strong><strong>Answer &#8211; <\/strong>All objects fall on ground with constant acceleration, called acceleration due to gravity (in the absence of air resistances). It is constant and does not depend upon the mass of an object. Hence, heavy objects do not fall faster than light objects.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\"><strong>3. What is the magnitude of the gravitational force between the earth and a 1 kg object on its surface? (Mass of the earth is 6 \u00d7 10<sup>24<\/sup>\u00a0kg and radius of the earth is 6.4 \u00d7 10<sup>6<\/sup>m.)<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><b>Answer &#8211; <\/b>According to the universal law of gravitation, gravitational force exerted on an object of mass m is given by:<br \/>\n<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\">F = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{(Gm_1m_2)}{r^2}\" alt=\"\\frac{(Gm_1m_2)}{r^2}\" align=\"absmiddle\" \/><br \/>\nHere<br \/>\nm<sub>1<\/sub> = Mass of Earth = 6.0 \u00d7 10<sup>24<\/sup> kg<br \/>\nm<sub>2<\/sub> = Mass of the body = 1 kg<br \/>\nr = Distance between the two bodies<br \/>\nRadius of Earth = 6.4 \u00d7 10<sup>6<\/sup> m<br \/>\nG = Universal gravitational constant = 6.6 \u00d7 10<sup>-11<\/sup> Nm<sup>2<\/sup>kg<sup>-2<br \/>\n<\/sup>By substituting all the values in the equation<br \/>\nF = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{(Gm_1m_2)}{r^2}\" alt=\"\\frac{(Gm_1m_2)}{r^2}\" align=\"absmiddle\" \/><\/span><\/p>\n<p>F = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{6.67\\times10^{-11}&amp;space;\\times&amp;space;6.0\\times&amp;space;10^{24}\\times&amp;space;1}{(6.4\\times&amp;space;10^6)^2}\" alt=\"\\frac{6.67\\times10^{-11} \\times 6.0\\times 10^{24}\\times 1}{(6.4\\times 10^6)^2}\" align=\"absmiddle\" \/><br \/>\nF = 9.8 N<br \/>\nThis Shows that Earth\u00a0exerts a force of 9.8 N on a body of mass 1 kg. the body will exert an equal force of attraction of 9.8 N on the Earth.<\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\"><strong>4. The earth and the moon are attracted to each other by gravitational force. Does the earth attract the moon with a force that is greater or smaller or the same as the force with which the moon attracts the earth? Why?<br \/>\n<\/strong><strong>Answer &#8211; <\/strong>According to the universal law of gravitation, two objects attract each other with equal force, but in opposite directions. The Earth attracts the moon with an equal force with which the mcn)n attracts the earth.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\"><strong>5. If the moon attracts the earth, why does the earth not move towards the moon?<br \/>\n<\/strong><strong>Answer &#8211;\u00a0<\/strong>The Earth and the moon experience equal gravitational forces from each other. However, the mass of the Earth is much larger than the mass of the moon. Hence, it accelerates at a rate lesser than the acceleration rate of the moon towards the Earth. For this reason, the Earth does not move towards the moon.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\"><strong>6. What happens to the force between two objects, if<br \/>\n<\/strong><strong>(i) <\/strong>The mass of one object is doubled?<br \/>\n<strong>(ii) <\/strong>The distance between the objects is doubled and tripled?<br \/>\n<strong>(iii) <\/strong>The masses of both objects are doubled?<br \/>\n<strong>Answer &#8211;<br \/>\n<\/strong><strong>(i)<\/strong> If the mass of one object is doubled, the force between two objects will be doubled (increases).<br \/>\n<strong>(ii)\u00a0<\/strong>If the distance been the objects is doubled the force between two objects will be one-fourth and if the distance will be tripled, the force will be one-ninth (1\/9).<br \/>\n<strong>(iii) <\/strong>If the masses of both objects are doubled the force will be 4 times. As F \u221d <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{m_1m_2}{r^2}\" alt=\"\\frac{m_1m_2}{r^2}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\"><strong>7. What is the importance of universal law of gravitation?<br \/>\n<\/strong><strong>Answer &#8211;\u00a0<\/strong>The universal law of gravitation explains many phenomena that were believed to be unconnected:<br \/>\n<strong>(i)<\/strong> The motion of the moon round the earth<br \/>\n<strong>(ii)<\/strong> The responsibility of gravity on the weight of the body which keeps us on the ground<br \/>\n<strong>(iii)<\/strong> The tides because of the moon and therefore the Sun<br \/>\n<strong>(iv)<\/strong> The motion of planets round the Sun<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\"><strong>8. What is the acceleration of free fall?<br \/>\n<\/strong><strong>Answer &#8211;\u00a0<\/strong>When objects fall towards the Earth under the effect of gravitational force alone, then they are said to be in free fall. Acceleration of free fall is 9.8 m s<sup>-2<\/sup>, which is constant for all objects (irrespective of their masses).<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\"><strong>9. What do we call the gravitational force between the earth and an object?<br \/>\n<\/strong><strong>Answer &#8211;\u00a0<\/strong>The gravitation force between the earth and an object is called weight. Weight is equal to the product of acceleration due to the gravity and mass of the object.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\"><strong>10. Amit buys few grams of gold at the poles as per the instruction of one of his friends. He hands over the same when he meets him at the equator. Will the friend agree with the weight of gold bought? If not, why? [Hint: The value of g is greater at the poles than at the equator.]<br \/>\n<\/strong><strong>Answer &#8211;\u00a0<\/strong>Weight of a body on the Earth is given by:<br \/>\nW = mg Where,<br \/>\nm = Mass of the body<br \/>\ng = Acceleration due to gravity.<br \/>\nThe value of g is greater at poles than at the equator. Therefore, gold at the equator weighs less than at the poles. Hence, Amit&#8217;s friend will not agree with the weight of the gold bought.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\"><strong>11. Why will a sheet of paper fall slower than one that is crumpled into a ball?<br \/>\n<\/strong><strong>Answer &#8211;\u00a0<\/strong>When a sheet of paper is crumbled into a ball, then its density increases. Hence, resistance to its motion through the air decreases and it falls faster than the sheet of paper.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>12. Gravitational force on the surface of the moon is only 1\/6 as strong as gravitational force on the earth. What is the weight in newton\u2019s of a 10 kg object on the moon and on the earth?<br \/>\n<\/strong><strong>Answer &#8211;\u00a0<\/strong>Weight of an object on the moon\u00a0<span id=\"MathJax-Element-1-Frame\" class=\"mjx-chtml MathJax_CHTML\" style=\"box-sizing: border-box; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: 400; font-size: 18.08px; letter-spacing: normal; overflow-wrap: normal; word-spacing: 0px; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; font-variant-ligatures: normal; font-variant-caps: normal; orphans: 2; widows: 2; -webkit-text-stroke-width: 0px; background-color: #ffffff; position: relative;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mo&gt;=&lt;\/mo&gt;&lt;mfrac&gt;&lt;mn&gt;1&lt;\/mn&gt;&lt;mn&gt;6&lt;\/mn&gt;&lt;\/mfrac&gt;&lt;mo&gt;&amp;#x00D7;&lt;\/mo&gt;&lt;\/math&gt;\"><span id=\"MJXc-Node-1\" class=\"mjx-math\" aria-hidden=\"true\"><span id=\"MJXc-Node-2\" class=\"mjx-mrow\"><span id=\"MJXc-Node-3\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{6}\" alt=\"\\frac{1}{6}\" align=\"absmiddle\" \/><\/span><\/span><\/span><\/span><span class=\"MJX_Assistive_MathML\" role=\"presentation\">\u00d7<\/span><\/span>Weight of an object on the Earth Also, Weight = Mass x <span style=\"font-size: 12pt;\">Acceleration Acceleration due to gravity, g = 9.8 m\/s<sup>2<\/sup> .<\/span><br \/>\n<span style=\"font-size: 12pt;\">Therefore, weight of a 10 kg object on the Earth = 10 <span id=\"MathJax-Element-1-Frame\" class=\"mjx-chtml MathJax_CHTML\" style=\"box-sizing: border-box; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: 400; letter-spacing: normal; overflow-wrap: normal; word-spacing: 0px; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; font-variant-ligatures: normal; font-variant-caps: normal; orphans: 2; widows: 2; -webkit-text-stroke-width: 0px; background-color: #ffffff; position: relative;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mo&gt;=&lt;\/mo&gt;&lt;mfrac&gt;&lt;mn&gt;1&lt;\/mn&gt;&lt;mn&gt;6&lt;\/mn&gt;&lt;\/mfrac&gt;&lt;mo&gt;&amp;#x00D7;&lt;\/mo&gt;&lt;\/math&gt;\"><span class=\"MJX_Assistive_MathML\" role=\"presentation\">\u00d7\u00a0<\/span><\/span><\/span><\/span><span style=\"font-family: georgia, palatino, serif; font-size: 12pt;\">9.8 = 98 N And, weight of the same object on the moon <span id=\"MathJax-Element-2-Frame\" class=\"mjx-chtml MathJax_CHTML\" style=\"box-sizing: border-box; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: 400; letter-spacing: normal; overflow-wrap: normal; word-spacing: 0px; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; font-variant-ligatures: normal; font-variant-caps: normal; orphans: 2; widows: 2; -webkit-text-stroke-width: 0px; background-color: #ffffff; position: relative;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mo&gt;=&lt;\/mo&gt;&lt;mfrac&gt;&lt;mn&gt;1&lt;\/mn&gt;&lt;mn&gt;6&lt;\/mn&gt;&lt;\/mfrac&gt;&lt;mo&gt;&amp;#x00D7;&lt;\/mo&gt;&lt;mn&gt;98&lt;\/mn&gt;&lt;mo&gt;=&lt;\/mo&gt;&lt;mn&gt;16.3&lt;\/mn&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;N&lt;\/mi&gt;&lt;\/mrow&gt;&lt;\/math&gt;\"><span id=\"MJXc-Node-8\" class=\"mjx-math\" aria-hidden=\"true\"><span id=\"MJXc-Node-9\" class=\"mjx-mrow\"><span id=\"MJXc-Node-10\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">= <span style=\"font-family: georgia, palatino, serif;\"><span id=\"MathJax-Element-1-Frame\" class=\"mjx-chtml MathJax_CHTML\" style=\"box-sizing: border-box; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: 400; font-size: 18.08px; letter-spacing: normal; overflow-wrap: normal; word-spacing: 0px; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; font-variant-ligatures: normal; font-variant-caps: normal; orphans: 2; widows: 2; -webkit-text-stroke-width: 0px; background-color: #ffffff; position: relative;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mo&gt;=&lt;\/mo&gt;&lt;mfrac&gt;&lt;mn&gt;1&lt;\/mn&gt;&lt;mn&gt;6&lt;\/mn&gt;&lt;\/mfrac&gt;&lt;mo&gt;&amp;#x00D7;&lt;\/mo&gt;&lt;\/math&gt;\"><span id=\"MJXc-Node-1\" class=\"mjx-math\" aria-hidden=\"true\"><span id=\"MJXc-Node-2\" class=\"mjx-mrow\"><span id=\"MJXc-Node-3\" class=\"mjx-mo\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{6}\" alt=\"\\frac{1}{6}\" align=\"absmiddle\" \/> <\/span><\/span><\/span><\/span><\/span><\/span><\/span><span id=\"MJXc-Node-14\" class=\"mjx-mo MJXc-space2\"><span class=\"mjx-char MJXc-TeX-main-R\">\u00d7 <\/span><\/span><span id=\"MJXc-Node-15\" class=\"mjx-mn MJXc-space2\"><span class=\"mjx-char MJXc-TeX-main-R\">98 <\/span><\/span><span id=\"MJXc-Node-16\" class=\"mjx-mo MJXc-space3\"><span class=\"mjx-char MJXc-TeX-main-R\">= <\/span><\/span><span id=\"MJXc-Node-17\" class=\"mjx-mn MJXc-space3\"><span class=\"mjx-char MJXc-TeX-main-R\">16.3<\/span><\/span><span id=\"MJXc-Node-18\" class=\"mjx-texatom\"><span id=\"MJXc-Node-19\" class=\"mjx-mrow\"><span id=\"MJXc-Node-20\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-main-R\">N<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>13. A ball is thrown vertically upwards with a velocity of 49 m\/s.<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>Calculate<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(i) <\/strong>The maximum height to which it rises,<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(ii) <\/strong>The total time it takes to return to the surface of the earth.<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>Answer &#8211;<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\">Initial velocity u = 49 m\/s<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Final speed v at maximum height = 0<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Acceleration due to earth gravity g = -9.8 m\/s<sup>2<\/sup>\u00a0(thus negative as ball is thrown up).<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(i) the maximum height to which it rises,<br \/>\n<\/strong>By third equation of motion,<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">2gH = v<sup>2<\/sup>\u00a0\u2013 u<sup>2<br \/>\n<\/sup><\/span><span style=\"font-family: georgia, palatino, serif;\">2 \u00d7 (- 9.8) \u00d7 H = 0 \u2013 (49)<sup>2<br \/>\n<\/sup><\/span><span style=\"font-family: georgia, palatino, serif;\">\u2013 19.6 H = \u2013 2401<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">H = 122.5 m<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>(ii) the total time it takes to return to the surface of the earth.<\/strong><br \/>\nTotal time T = Time to ascend (T<sub>a<\/sub>) + Time to descend (T<sub>d<\/sub>)<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">v = u + gt<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">0 = 49 + (-9.8) x T<sub>a<br \/>\n<\/sub><\/span><span style=\"font-family: georgia, palatino, serif;\">Ta = (49\/9.8) = 5 s<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Also, T<sub>d<\/sub> = 5 s<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Therefore T = T<sub>a<\/sub>\u00a0+ T<sub>d<br \/>\n<\/sub><\/span><span style=\"font-family: georgia, palatino, serif;\">T = 5 + 5<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">T = 10 s<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>14. A stone is released from the top of a tower of height 19.6 m. Calculate its final velocity just before touching the ground.<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>Answer &#8211;<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\">Initial velocity <\/span><span style=\"font-family: georgia, palatino, serif;\">u = 0<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Tower height = total distance = 19.6m<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">g = 9.8 m\/s<sup>2<br \/>\n<\/sup><\/span><span style=\"font-family: georgia, palatino, serif;\">Consider third equation of motion<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">v<sup>2<\/sup>\u00a0= u<sup>2<\/sup>\u00a0+ 2gs<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">v<sup>2\u00a0<\/sup>= 0 + 2 \u00d7 9.8 \u00d7 19.6<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">v<sup>2<\/sup>\u00a0= 384.16<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">v = \u221a(384.16)<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">v = 19.6m\/s<br \/>\n<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>15. A stone is thrown vertically upward with an initial velocity of 40 m\/s. Taking g = 10 m\/s<sup>2<\/sup>, find the maximum height reached by the stone. What is the net displacement and the total distance covered by the stone?<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>Answer &#8211;<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\">Initial velocity u = 40m\/s<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">g = 10 m\/s<sup>2<br \/>\n<\/sup><\/span><span style=\"font-family: georgia, palatino, serif;\">Max height final velocity = 0<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Consider third equation of motion<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">v<sup>2<\/sup>\u00a0= u<sup>2<\/sup>\u00a0\u2013 2gs [negative as the object goes up]<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">0 = (40)<sup>2<\/sup> \u2013 2 \u00d7 10 \u00d7 s<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">s = (40 \u00d7 40) \/ 20<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Maximum height s = 80m<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Total Distance = s + s = 80 + 80<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Total Distance = 160m<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Total displacement = 0 (The first point is the same as the last point)<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>16. Calculate the force of gravitation between the earth and the Sun, given that the mass of the earth = 6 \u00d7 10<sup>24<\/sup>\u00a0kg and of the Sun = 2 \u00d7 10<sup>30<\/sup>\u00a0kg. The average distance between the two is 1.5 \u00d7 10<sup>11<\/sup> m.<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>Answer &#8211;<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\">Mass of the sun m<sub>s<\/sub>\u00a0= 2 \u00d7 10<sup>30<\/sup>\u00a0kg<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Mass of the earth m<sub>e<\/sub>\u00a0= 6 \u00d7 10<sup>24<\/sup>\u00a0kg<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Gravitation constant G = 6.67 x 10<sup>-11<\/sup>\u00a0N m<sup>2<\/sup>\/ kg<sup>2<br \/>\n<\/sup><\/span><span style=\"font-family: georgia, palatino, serif;\">Average distance r = 1.5 \u00d7 10<sup>11<\/sup>\u00a0m<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Consider Universal law of Gravitation<br \/>\nF = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{(Gm_1m_2)}{r^2}\" alt=\"\\frac{(Gm_1m_2)}{r^2}\" align=\"absmiddle\" \/><\/span><\/span><\/p>\n<p>F = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{6.67\\times&amp;space;10^{-11}&amp;space;\\times&amp;space;6\\times&amp;space;10^{24}\\times&amp;space;2\\times&amp;space;10^{30}}{(1.5\\times&amp;space;10^{11})^2}\" alt=\"\\frac{6.67\\times 10^{-11} \\times 6\\times 10^{24}\\times 2\\times 10^{30}}{(1.5\\times 10^{11})^2}\" align=\"absmiddle\" \/><br \/>\n= 3.56 \u00d7 10<sup>22\u00a0<\/sup>N<\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>17. A stone is allowed to fall from the top of a tower 100 m high and at the same time another stone is projected vertically upwards from the ground with a velocity of 25 m\/s. Calculate when and where the two stones will meet.<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>Answer &#8211; <\/strong>Let the two stones meet after a time t.<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">(i) When the stone from the top of the tower is thrown,<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Initial velocity u\u2019 = 0<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Distance travelled = x<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Time taken = t<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Therefore,<br \/>\ns = ut + <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{2}\" alt=\"\\frac{1}{2}\" align=\"absmiddle\" \/> gt<sup>2<\/sup><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">x = 0 + <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{2}\" alt=\"\\frac{1}{2}\" align=\"absmiddle\" \/> gt<sup>2<\/sup><br \/>\nx = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{2}\" alt=\"\\frac{1}{2}\" align=\"absmiddle\" \/>\u00a0 \u00d7 9.8 \u00d7 t<sup>2\u00a0<\/sup><br \/>\nx = 4.9 t<sup>2\u00a0<\/sup>&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;- (i)<br \/>\n<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>(ii)<\/strong> When the stone is thrown upwards,<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Initial velocity u = 25 m\/s<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Distance travelled = (100 \u2013 x)<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Time taken = t<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">s = ut &#8211; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{2}\" alt=\"\\frac{1}{2}\" align=\"absmiddle\" \/> gt<sup>2<\/sup><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">(100 &#8211; x) = 25t &#8211;\u00a0 <span style=\"font-family: georgia, palatino, serif;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{2}\" alt=\"\\frac{1}{2}\" align=\"absmiddle\" \/> \u00d7 10 t<sup>2<br \/>\n<\/sup>x = 100 &#8211; 25t + 5t<sup>2<\/sup>\u00a0 \u00a0 \u00a0 &#8212;&#8212;&#8212;&#8212;&#8212;&#8211; (ii)<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">From equations (i) and (ii)<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">5t<sup>2<\/sup>\u00a0= 100 -25t + 5t<sup>2<br \/>\n<\/sup><\/span><span style=\"font-family: georgia, palatino, serif;\">t = (100\/25) = 4sec.<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">After 4sec, two stones will meet<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">From (i)<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">x = 5t<sup>2<\/sup> = 5 \u00d7 4 \u00d7 4 = 80m.<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Putting the value of x in (100 &#8211; x)<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">= (100-80) = 20m.<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">This means that after 4sec, 2 stones meet a distance of 20 m from the ground.<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>18. A ball thrown up vertically returns to the thrower after 6 s. Find<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(a) <\/strong>The velocity with which it was thrown up,<strong><br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(b)<\/strong> The maximum height it reaches, and<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(c) <\/strong>Its position after 4s.<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>Answer &#8211;<br \/>\n<\/strong><\/span>u = ?<\/span><br \/>\n<span style=\"color: #000000;\">v = 0 <\/span><br \/>\n<span style=\"color: #000000;\">g = 10 m\/s<sup>2<\/sup>\u00a0<\/span><br \/>\n<span style=\"color: #000000;\">Total time = 6 s (to go up and down) <\/span><br \/>\n<span style=\"color: #000000;\">\u2234 Time for upward journey = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{6}{2}\" alt=\"\\frac{6}{2}\" align=\"absmiddle\" \/> = 3 s<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>(a)<\/strong> Final velocity at maximum height v = 0<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">From first equation of motion:-<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">v = u \u2013 gt<sub>a<br \/>\n<\/sub><\/span><span style=\"font-family: georgia, palatino, serif;\">u = v + gt<sub>a<br \/>\n<\/sub><\/span><span style=\"font-family: georgia, palatino, serif;\">= 0 + 10 x 3<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">= 30m\/s<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">The velocity with which stone was thrown up is 30m\/s.<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>(b)<\/strong> From second equation of motion<br \/>\ns = ut<sub>a<\/sub> &#8211; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{2}\" alt=\"\\frac{1}{2}\" align=\"absmiddle\" \/>g(t<sub>a<\/sub>)<sup>2<\/sup><br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">= 30 \u00d7 3 &#8211; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{2}\" alt=\"\\frac{1}{2}\" align=\"absmiddle\" \/> \u00d7 10 \u00d7 (3)<sup>2<\/sup><br \/>\n= 90 &#8211; 45<br \/>\n= 45 m<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">The maximum height stone reaches is 45m.<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>(c)<\/strong> In 3sec, it reaches the maximum height.<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Distance travelled in another 1sec = s\u2019<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">s = ut<sub>a<\/sub> &#8211; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{2}\" alt=\"\\frac{1}{2}\" align=\"absmiddle\" \/>g(t<sub>a<\/sub>)<sup>2<\/sup><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\">s =0 &#8211; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{2}\" alt=\"\\frac{1}{2}\" align=\"absmiddle\" \/> (-10)(1)<sup>2<\/sup><br \/>\n= 0 + 5<br \/>\n= 5 m<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">The distance travelled in another 1sec = 5m.<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Therefore in 4sec, the position of point p (45 \u2013 5)<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">= 40m from the ground.<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>19. In what direction does the buoyant force on an object immersed in a liquid act?<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>Answer &#8211;\u00a0<\/strong>An object immersed in a liquid experiences buoyant force in the upward direction.<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>20. Why a block of plastic when released under water come up to the surface of water?<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>Answer &#8211;\u00a0<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\">The density of plastic is lesser than that of water. Therefore, the force of buoyancy on plastic block will be greater than the weight of plastic block. Hence, the acceleration of plastic block is going to be in the upward direction. So, the plastic block comes up to the surface of water.<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>21. The volume of 50 g of a substance is 20 cm<sup>3<\/sup>. If the density of water is 1 g cm<sup>\u20133<\/sup>, will the substance float or sink?<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>Answer &#8211; <\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\">To find the Density of the substance the formula is<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Density = (Mass\/Volume)<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Density = (50\/20) = 2.5g\/cm<sup>3<br \/>\n<\/sup><\/span><span style=\"font-family: georgia, palatino, serif;\">Density of water = 1g\/cm<sup>3<br \/>\n<\/sup><\/span><span style=\"font-family: georgia, palatino, serif;\">Density of the substance is greater than density of water. So the substance will sink.<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>22. The volume of a 500 g sealed packet is 350 cm<sup>3<\/sup>. Will the packet float or sink in water if the density of water is 1 g cm<sup>\u20133<\/sup>? What will be the mass of the water displaced by this packet?<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>Answer &#8211;<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\">Density of sealed packet = 500\/350 = 1.42 g\/cm<sup>3<br \/>\n<\/sup><\/span><span style=\"font-family: georgia, palatino, serif;\">Density of sealed packet is greater than density of water<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Therefore the packet will sink.<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Considering Archimedes Principle,<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Displaced water volume = Force exerted on the sealed packet.<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Volume of water displaced = 350cm<sup>3<br \/>\n<\/sup><\/span><span style=\"font-family: georgia, palatino, serif;\">Therefore displaced water mass = \u03c1 x V<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">= 1 \u00d7 350<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Mass of displaced water = 350g.<\/span><\/span><\/p>\n<p><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-science\/\" target=\"_blank\" rel=\"noopener\"><b><i>Go Back To Chapters<\/i><\/b><\/a><\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions Class 9 Science\u00a0 The NCERT Solutions in English Language for Class 9 Science Chapter &#8211; 10 (Gravitation) has been provided here to help the students in solving the questions from this exercise.\u00a0 Chapter &#8211; 10 (Gravitation)\u00a0 Questions 1. State the universal law of gravitation. Answer &#8211; Every object in the universe attracts every [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[729],"tags":[730,750,751,733,5],"class_list":["post-5045","post","type-post","status-publish","format-standard","hentry","category-class-9-science","tag-class-9-ncert-solutions","tag-ncert-class-9-science-chapter-10-gravitation","tag-ncert-solutions-class-9-science-chapter-10-in-english","tag-ncert-solutions-class-9-science-in-english","tag-ncert-solutions-in-english"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.9 (Yoast SEO v27.4) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>NCERT Solutions Class 9 Science Chapter 10 Gravitation | TheExamPillar NCERT<\/title>\n<meta name=\"description\" content=\"NCERT Solutions Class 9 Science\u00a0The NCERT Solutions in English Language for Class 9 Science Chapter - 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