All STD 11 - Gravitation questions
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- 101. A body of mass (\(2 {M}\)) splits into four masses \(\{{m}, {M}-{m}, {m}, {M}-{m}\}\), which are rearranged to form a square as shown in the figure. The ratio of \(\frac{{M}}{{m}}\) for which, the gravitational potential energy of the system becomes maximum is \({x}: 1\). The value of \(x\) is ..... .
2021 Hard - 102. A body weights \(49\,N\) on a spring balance at the north pole. ..... \(N\) will be its weight recorded on the same weighing machine, if it is shifted to the equator? (Use \(g=\frac{G M}{R^{2}}=9.8 \,ms ^{-2}\) and radius of earth, \(R =6400\, km .]\) 2021 Medium
- 103. A geostationary satellite is orbiting around an arbitary planet \(^{\prime} P ^{\prime}\) at a height of \(11 R\) above the surface of \(^{\prime} P ^{\prime} ,\) \(R\) being the radius of \(^{\prime} P .^{\prime}\) The time period of another satellite in hours at a height of \(2R\) from the surface of \(^{\prime} P ^{\prime}\) is \(........\).\(^{\prime} P ^{\prime}\) has the time period of \(24\, hours.\) 2021 Medium
- 104. A mass of \(50\, {kg}\) is placed at the centre of a uniform spherical shell of mass \(100\, {kg}\) and radius \(50 \,{m}\). If the gravitational potential at a point, \(25\, {m}\) from the centre is \({V} \,{kg} / {m} .\) The value of \({V}\) is 2021 Medium
- 105. A person whose mass is \(100\, {kg}\) travels from Earth to Mars in a spaceship. Neglect all other objects in sky and take acceleration due to gravity on the surface of the Earth and Mars as \(10\) \({m} / {s}^{2}\) and \(4 \,{m} / {s}^{2}\) respectively. Identify from the below figures, the curve that fits best for the weight of the passenger as a function of time.
2021 Medium - 106. A planet revolving in elliptical orbit has \((A)\) a constant velocity of revolution. \((B)\) has the least velocity when it is nearest to the sun. \((C)\) its areal velocity is directly proportional to its velocity. \((D)\) areal velocity is inversely proportional to its velocity. \((E)\) to follow a trajectory such that the areal velocity is constant. Choose the correct answer from the options given below 2021 Hard
- 107. A satellite is launched into a circular orbit of radius \(‘R’\) around earth while a second satellite is launched into an orbit of radius \(1.02 R\). The percentage difference in the time periods of the two satellites is ......... \(\%\) 2021 Medium
- 108. A solid sphere of radius \(R\) gravitationally attracts a particle placed at \(3 R\) form its centre with a force \(F _{1}\). Now a spherical cavity of radius \(\left(\frac{ R }{2}\right)\) is made in the sphere (as shown in figure) and the force becomes \(F _{2}\). The value of \(F _{1}: F _{2}\) is
2021 Hard - 109. Consider a binary star system of star \(A\) and star \(B\) with masses \(m_{A}\) and \(m_{B}\) revolving in a circular orbit of radii \(r_{A}\) and \(r_{B}\), respectively. If \(T_{A}\) and \(T_{B}\) are the time period of star \(A\) and star \(B\), respectively, then - 2021 Medium
- 110. Consider a planet in some solar system which has a mass double the mass of earth and density equal to the average density of earth. If the weight of an object on earth is \({W}\), then weight of the same object on that planet will be 2021 Medium
- 111. Consider two satellites \(S_{1}\) and \(S_{2}\) with periods of revolution \(1\, hr\). and \(8\, hr\). respectively revolving around a planet in circular orbits. The ratio of angular velocity of satellite \(S_{1}\) to the angular velocity of satellites \(S _{2}\) is 2021 Medium
- 112. Find the gravitational force of attraction between the ring and sphere as shown in the diagram, where the plane of the ring is perpendicular to the line joining the centres. If \(\sqrt{8}\, R\) is the distance between the centres of a \(mng\) (of mass ' \(m\) ) and a sphere (mass ' \(M\) ) where both have equal radius \('R'.\)
2021 Hard - 113. Given below are two statements: one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion \(A :\) The escape velocities of planet \(A\) and \(B\) are same. But \(A\) and \(B\) are of unequal mass. Reason \(R :\) The product of their mass and radius must be same, \(M _{1} R _{1}= M _{2} R _{2}\) In the light of the above statements, choose the most appropriate answer from the options given below 2021 Medium
- 114. If one wants to remove all the mass of the earth to infinity in order to break it up completely. The amount of energy that needs to be supplied will be \(\frac{x}{5}\, \frac{ GM ^{2}}{ R }\) where \(x\) is \(\quad\,..........\) (Round off to the Nearest Integer) (\(M\) is the mass of earth, \(R\) is the radius of earth, \(G\) is the gravitational constant) 2021 Hard
- 115. If \({R}_{{E}}\) be the radius of Earth, then the ratio between the acceleration due to gravity at a depth \(' {r} '\) below and a height \(' r '\) above the earth surface is: (Given : \(\left.{r}<{R}_{{E}}\right)\) 2021 Medium
- 116. If the angular velocity of earth's spin is increased such that the bodies at the equator start floating, the duration of the day would be approximately ........ minutes (Take : \(g =10 \,ms ^{-2},\) the radius of earth, \(R =6400 \times 10^{3}\, m ,\) Take \(\left.\pi=3.14\right)\) 2021 Medium
- 117. In the reported figure of earth, the value of acceleration due to gravity is same at point \(A\) and \(C\) but it is smaller than that of its value at point \(B\) (surface of the earth). The value of OA \(: AB\) will be \(x : y .\) The value of \(x\) is \(\ldots \ldots \ldots\)
2021 Hard - 118. Inside a uniform spherical shell \((a)\) the gravitational field is zero \((b)\) the gravitational potential is zero \((c)\) the gravitational field is same everywhere \((d)\) the gravitation potential is same everywhere \((e)\) all of the above Choose the most appropriate answer from the options given below 2021 Medium
- 119. Suppose two planets (spherical in shape) of radii \({R}\) and \(2 {R}\), but mass \({M}\) and \(9\, {M}\) respectively have a centre to centre separation \(8\, {R}\) as shown in the figure. A satellite of mass \('{m}'\) is projected from the surface of the planet of mass \('M'\) directly towards the centre of the second planet. The minimum speed \('v'\) required for the satellite to reach the surface of the second planets is \(\sqrt{\frac{a}{7} \frac{G M}{R}}\) then the value of \('a'\) is \(....\) [Given: The two planets are fixed in their position]
2021 Hard - 120. The acceleration due to gravity is found upto an accuracy of \(4 \,\%\) on a planet. The energy supplied to a simple pendulum to known mass ' \({m}\) ' to undertake oscillations of time period \(T\) is being estimated. If time period is measured to an accuracy of \(3\, \%\), the accuracy to which \({E}\) is known as \(..........\,\%\) 2021 Hard
- 121. The angular momentum of a planet of mass \(M\) moving around the sun in an elliptical orbit is \(\overrightarrow{ L }\). The magnitude of the areal velocity of the planet is: 2021 Medium
- 122. The initial velocity \(v_{i}\) required to project a body vertically upward from the surface of the earth to reach a height of \(10\, R ,\) where \(R\) is the radius of the earth, may be described in terms of escape velocity \(v_{ e }\) such that \(v_{i}=\sqrt{\frac{x}{y}} \times v_{ e } .\) The value of \(x\) will be ...... . 2021 Hard
- 123. The masses and radii of the earth and moon are \(\left({M}_{1}, {R}_{1}\right)\) and \(\left({M}_{2}, {R}_{2}\right)\) respectively. Their centres are at a distance ' \({r}\) ' apart. Find the minimum escape velocity for a particle of mass ' \({m}\) ' to be projected from the middle of these two masses: 2021 Hard
- 124. The maximum and minimum distances of a comet from the Sun are \(1.6 \times 10^{12}\, m\) and \(8.0 \times 10^{10}\, m\) respectively. If the speed of the comet at the nearest point is \(6 \times 10^{4}\, ms ^{-1},\) the speed at the farthest point is ......... \(\times 10^{3}\, m / s\) 2021 Medium
- 125. The planet Mars has two moons, if one of them has a period \(7\, hours,\, 30\, minutes\) and an orbital radius of \(9.0 \times 10^{3}\, {km} .\) Find the mass of Mars. \(\left\{\operatorname{Given} \frac{4 \pi^{2}}{G}=6 \times 10^{11} {N}^{-1} {m}^{-2} {kg}^{2}\right\}\) 2021 Medium
- 126. The radius in kilometer to which the present radius of earth \(( R =6400\, km )\) to be compressed so that the escape velocity is increased \(10\) time is ............\(km\) 2021 Medium
- 127. The time period of a satellite in a circular orbit of radius \(R\) is \(T\). The period of another satellite in a circular orbit of radius \(9 R\) is............ \(T\) 2021 Medium
- 128. Two identical particles of mass \(1\, {kg}\) each go round a circle of radius \({R}\), under the action of their mutual gravitational attraction. The angular speed of each particle is : 2021 Medium
- 129. Two satellites \(A\) and \(B\) of masses \(200\, kg\) and \(400\, kg\) are revolving round the earth at height of \(600\, km\) and \(1600\, km\) respectively. If \(T _{ A }\) and \(T _{ B }\) are the time periods of \(A\) and \(B\) respectively then the value of \(T _{ B }- T _{ A }\) [Given : radius of earth \(=6400\, km\), mass of earth \(=6 \times 10^{24}\, kg\) ]
2021 Hard - 130. Two satellites revolve around a planet in coplanar circular orbits in anticlockwise direction. Their period of revolutions are \(1\, hour\) and \(8\, hours\) respectively. The radius of the orbit of nearer satellite is \(2 \times 10^{3}\, {km}\). The angular speed of the farther satellite as observed from the nearer satellite at the instant when both the satellites are closest is \(\frac{\pi}{{x}}\, {rad} \,{h}^{-1}\) where \({x}\) is ..... . 2021 Hard
- 131. Two stars of masses \(m\) and \(2\, m\) at a distance \(d\) rotate about their common centre of mass in free space. The period of revolution is 2021 Hard
- 132. A body is moving in a low circular orbit about a planet of mass \(M\) and radius \(R\). The radius of the orbit can be taken to be \(R\) it self. Then the ratio of the speed of this body in the orbit to the escape velocity from the planet is 2020 Medium
- 133. A box weighs \(196 \;\mathrm{N}\) on a spring balance at the north pole. Its weight recorded on the same balance if it is shifted to the equator is close to ....... \(N\) (Take \(\mathrm{g}=10\; \mathrm{ms}^{-2}\) at the north pole and the radius of the earth \(=6400\; \mathrm{km}\)) 2020 Medium
- 134. A satellite is in an elliptical orbit around a planet \(P.\) It is observed that the velocity of the satellite when it is farthest from the planet is \(6\) time less than that when it is closest to the planet. The ratio of distances between the satellite and the planet at closest and farthest points is\(......\) 2020 Medium
- 135. A satellite is moving in a low nearly circular orbit around the earth. Its radius is roughly equal to that of the earth's radius \(R _{ e }\). By firing rockets attached to it, its speed is instantaneously increased in the direction of its motion so that is become \(\sqrt{\frac{3}{2}}\) times larger. Due to this the farthest distance from the centre of the earth that the satellite reaches is \(R\), value of \(R\) is\(....R_e\) 2020 Hard
- 136. A satellite of mass \(\mathrm{m}\) is launched vertically upwards with an initial speed \(u\) from the surface of the earth. After it reaches height \(\mathrm{R}\) (\(R =\) radius of the earth), it ejects a rocket of mass \(\frac{\mathrm{m}}{10}\) so that subsequently the satellite moves in a circular orbit. The kinetic energy of the rocket is (\(G\) is the gravitational constant: \(\mathrm{M}\) is the mass of the earth) 2020 Hard
- 137. An asteroid is moving directly towards the centre of the earth. When at a distance of \(10 \mathrm{R}\) (\(R\) is the radius of the earth) from the earths centre, it has a speed of \(12 \;\mathrm{km} / \mathrm{s}\). Neglecting the effect of earths atmosphere, what will be the speed of the asteroid when it hits the surface of the earth (escape velocity from the earth is \(11.2 \;\mathrm{km} / \mathrm{s}\) ) \(?\) Give your answer to the nearest integer in \(km/s\) 2020 Hard
- 138. Consider two solid spheres of radii \(\mathrm{R}_{1}=1 \;\mathrm{m}\) \(\mathrm{R}_{2}=2\; \mathrm{m}\) and masses \(\mathrm{M}_{1}\) and \(\mathrm{M}_{2},\) respectively. The gravitational field due to sphere \((1)\) and \((2)\) are shown. The value of \(\frac{\mathrm{M}_{1}}{\mathrm{M}_{2}}\) is
2020 Medium - 139. On the \(x-\)axis and a dsitance \(x\) from the origin, the gravitational field due to a mass distribution is given by \(\frac{A x}{\left(x^{2}+a^{2}\right)^{3 / 2}}\) in the \(x-\)direction. The magnitude of gravitational potential on the \(x-\)axis at a distance \(x,\) taking its value to be zero at infinity, is 2020 Hard
- 140. Planet \(A\) has mass \(\mathrm{M}\) and radius \(\mathrm{R}\). Planet \(\mathrm{B}\) has half the mass and half the radius of Planet \(A\). If the escape velocities from the Planets \(A\) and \(\mathrm{B}\) are \(v_{\mathrm{A}}\) and \(v_{\mathrm{B}},\) respectively, then \(\frac{v_{\mathrm{A}}}{v_{\mathrm{B}}}=\frac{\mathrm{n}}{4}\) The value of \(\mathrm{n}\) is 2020 Medium
- 141. The acceleration due to gravity on the earth's surface at the poles is \(g\) and angular velocity of the earth about the axis passing through the pole is \(\omega .\) An object is weighed at the equator and at a height \(h\) above the poles by using a spring balance. If the weights are found to be same, then \(h\) is \(:( h << R ,\) where \(R\) is the radius of the earth) 2020 Hard
- 142. The height \({ }^{\prime} h ^{\prime}\) at which the weight of a body will be the same as that at the same depth \('h'\) from the surface of the earth is (Radius of the earth is \(R\) and effect of the rotation of the earth is neglected): 2020 Hard
- 143. The mass density of a planet of radius \(R\) varies with the distance \(r\) from its centre as \(\rho( r )=\rho_{0}\left(1-\frac{ r ^{2}}{ R ^{2}}\right) .\) Then the gravitational field is maximum at 2020 Hard
- 144. The mass density of a spherical galaxy varies as \(\frac{ K }{ r }\) over a large distance \('r'\) from its centre. In that region, a small star is in a circular orbit of radius \(R\). Then the period of revolution, \(T\) depends on \(R\) as 2020 Hard
- 145. The value of the acceleration due to gravity is \(g _{1}\) at a height \(h =\frac{ R }{2}( R =\) radius of the earth) from the surface of the earth. It is again equal to \(g _{1}\) at a depth \(d\) below the surface of the earth. The ratio \(\left(\frac{ d }{ R }\right)\) equals 2020 Hard
- 146. Two planets have masses \(M\) and \(16\, M\) and their radii are \(a\) and \(2\, a\) respectively. The separation between the centres of the planets is \(10\, a.\) A body of mass \(m\) is fired from the surface of the larger planet towards the smaller planet along the line joining their centres. For the body to be able to reach at the surface of smaller planet, the minimum firing speed needed is 2020 Hard
- 147. A rocket has to be launched from each in such a way that it never returns. If \(E\) is the minimum energy delivered by the rocket launcher, what should be the minimum energy that the launcher should have if the same rocket is to be launched from the surface of the moon ? Assume that the density of the earth and the moon are equal and that the earth’s volume is \(64\) times the volume of the moon. 2019 Hard
- 148. A satellite is moving with a constant speed \(v\) in circular orbit around the earth. An object of mass \(‘m’\) is ejected from the satellite such that it just escapes from the gravitational pull of the earth. At the time of ejection, the kinetic energy of the object is 2019 Medium
- 149. A satellite is revolving in a circular orbit at a height \(h\) from the earth surface, such that \(h < < R\) where \(R\) is the radius of the earth. Assuming that the effect of earth’s atmosphere can be neglected the minimum increase in the speed required so that the satellite could escape from the gravitational field of earth is 2019 Medium
- 150. A solid sphere of mass \(‘M’\) and radius \(‘a’\) is surrounded by a uniform concentric spherical shell of thickness \(2a\) and mass \(2M.\) The gravitational field at distance \(‘3a’\) from the centre will be 2019 Medium
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