Gravitation PYQs Set 6 (PDF)

Set 6 of 12 · Questions 151-180 of 351

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Mere Teacher · Previous Year Questions JEE Main Physics · Gravitation · Set 6 (Q151-180)
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151. $What is the minimum energy required to launch a satellite of mass m from the surface of a planet of mass M and radius R in a circular orbit at an altitude of 2R?$ (1) $\frac{5 GmM}{6 R}$ (2) $\frac{2 GmM}{3 R}$ (3) $\frac{GmM}{2 R}$ (4) $\frac{GmM}{3 R}$ 152. $A planet moving along an elliptical orbit is closest to the sun at a distance r_{1} and farthest away at a distance of r_{2} . If v_{1} and v_{2} are the linear velocities at these points respectively, then the ratio \frac{v _{1}}{v _{2}} is:$ (1) $(r_{1} / r_{2})^{2}$ (2) $r_{2} / r_{1}$ (3) $(r_{2} / r_{1})^{2}$ (4) $r_{1} / r_{2}$ 153. $A body weighs 300 N on the surface of the earth. How much will it weigh at a distance \frac{R}{2} below the surface of earth? (R \to Radius of earth)$ (1) $300 N$ (2) $250 N$ (3) $200 N$ (4) $150 N$ 154. $The acceleration due to gravity at a height 1 km above the earth is the same as at a depth d below the surface of earth. Then [NEET 2017]$ (1) $d = \frac{1}{2} km$ (2) $d = 1 km$ (3) $d = \frac{3}{2} km$ (4) $d = 2 km$ 155. $A test particle is moving in circular orbit in the gravitational field produced by a mass density r (r) = \frac{K}{r ^{2}} . Identify the correct relation between the radius R of the particle's orbit and its period T :$ (1) $T / R is a constant$ (2) $T^{2} / R^{3} is a constant$ (3) $T / R^{2} is a constant$ (4) $TR is a constant$ 156. $The mean radius of earth is R, its angular speed on its own axis is (f) and the acceleration due to gravity at earth’s surface is g . What will be the radius of the orbit of a geostationary satellite?$ (1) $(R^{2} g / ω^{2})^{1/3}$ (2) $(Rg / ω)^{2})^{1/3}$ (3) $(R^{2} ω^{2} / g)^{1/3}$ (4) $(R^{2} g / ω)^{1/3}$ 157. $A satellite is launched into a circular orbit of radius ' R' around the earth. A second satellite is launched into an orbit of radius 1.03 R. The time period of revolution of the second satellite is larger than the first one approximately by$ (1) $9 %$ (2) $3 %$ (3) $4.5 %$ (4) $2.5 %$ 158. $The value of acceleration due to gravity at a depth of 1600 km is equal to [Radius of earth 6400 km]$ (1) $9.8 m s^{- 2}$ (2) $4.9 m s^{- 2}$ (3) $7.35 m s^{- 2}$ (4) $19.6 m s^{- 2}$ 159. $The orbital velocity of a body near the surface of a planet ' A' is equal to escape velocity of a body from the planet ' B'. If the masses of planets A and B are same, the ratio of their radii is$ (1) $1$ (2) $\frac{1}{2}$ (3) $\frac{1}{3}$ (4) $2$ 160. $If a satellite orbiting the Earth is 9 times closer to the Earth than the Moon, what is the time period of rotation of the satellite? Given rotational time period of Moon = 27 days and gravitational attraction between the satellite and the moon is neglected.$ (1) $27 days$ (2) $1 day$ (3) $81 days$ (4) $3 days$ 161. $A body is moving in a low circular orbit about a planet of mass M and radius R . The radius of the orbit can be taken to be R itself. Then the ratio of the speed of this body in the orbit to the escape velocity from the planet is$ (1) $1$ (2) $2$ (3) $2$ (4) $\frac{1}{2}$ 162. $A particle is moving an X -axis has potential energy U = 2 - 20 x + 5 x^{2} J along X -axis. The particle is released at x = - 3 . The maximum value of x will be (x is in metre and U is in joules)$ (1) $5 m$ (2) $3 m$ (3) $7 m$ (4) $8 m$ 163. $Two bodies of masses m and 9 m are placed at a distance r . The gravitational potential at a point on the line joining them, where gravitational field is zero, is (G is universal gravitational constant)$ (1) $\frac{- 14 Gm}{r}$ (2) $\frac{- 16 Gm}{r}$ (3) $\frac{- 12 Gm}{r}$ (4) $\frac{- 8 Gm}{r}$ 164. $A planet of radius R = \frac{1}{10} \times (radius of Earth) has the same mass density as Earth. Scientists dig a well of depth \frac{R}{5} on it and lower a wire of the same length and of linear mass density 10-3 k g m^{-1} into it. If the wire is not touching anywhere, the force applied at the top of the wire by a person holding it in place is (take the radius of Earth = 6 \times 106 m and the acceleration due to gravity on Earth is 10 m s^{-2})$ (1) $96 N$ (2) $108N$ (3) $120N$ (4) $150N$ 165. $Two planets A and B of radii R and 1.5R have densities ρ and \frac{ρ}{2} respectively. The ratio of acceleration due to gravity at the surface of B to A is:$ (1) $2 : 3$ (2) $2 : 1$ (3) $3 : 4$ (4) $4 : 3$ 166. $A space ship orbits around a planet at a height of 20 km from its surface. Assuming that only gravitational field of the planet acts on the spaceship, what will be the number of complete revolutions made by the spaceship in 24 hours around the planet? [Given: Mass of Planet = 8 \times 10^{22} kg, Radius of planet = 2 \times 10^{6} m, Gravitational constant G = 6.67 \times 10^{- 11} Nm^{2} / kg^{2}]$ (1) $9$ (2) $17$ (3) $13$ (4) $11$ 167. $Assuming that the gravitational potential energy of an object at infinity is zero, the change in potential energy (final - initial) of an object of mass m, when taken to a height h from the surface of earth (of radius R) is given by, [NEET 2019]$ (1) $- \frac{GMm}{R + h}$ (2) $\frac{GMmh}{R ( R + h )}$ (3) $mgh$ (4) $\frac{GMm}{R + h}$ 168. $A body is projected with a velocity greater than orbital velocity but less than escape velocity. Its path is$ (1) $circular$ (2) $elliptical$ (3) $parabolic$ (4) $hyperbolic$ 169. $Two bodies of masses 4 m and 9 m are separated by a distance ' r'. The gravitational potential at a point on this line joining them where the gravitational field becomes zero is$ (1) $\frac{- 25 Gm}{r}$ (2) $\frac{- 4 Gm}{r}$ (3) $\frac{- 9 Gm}{r}$ (4) $\frac{- 13 Gm}{r}$ 170. $A rocket has to be launched from earth in such a way that it never returns. If E is the minimum energy delivered by the rocket launcher, what should be the minimum energy that the launcher should have if the same rocket is to be launched from the surface of the moon? Assume that the density of the earth and the moon are equal and that the earth's volume is 64 times the volume of the moon.$ (1) $\frac{E}{64}$ (2) $\frac{E}{32}$ (3) $\frac{E}{4}$ (4) $\frac{E}{16}$ 171. $A planet is moving in. a circular orbit. It completes 2 revolutions in 360 days. What is its angular frequency?$ (1) $1.5 \times 10^{- 2} rad / day$ (2) $2.5 \times 10^{- 2} rad / day$ (3) $3.5 \times 10^{- 2} rad / day$ (4) $4.5 \times 10^{- 2} rad / day$ 172. $A body is projected vertically from the surface of the earth of radius ' R' with velocity equal to half of the escape velocity. The maximum height reached by the body is$ (1) $\frac{R}{5}$ (2) $\frac{R}{3}$ (3) $\frac{R}{2}$ (4) $\frac{R}{4}$ 173. $The time period of a satellite revolving around earth in a given orbit is 7 hours. If the radius of orbit is increased to three times its previous value, then approximate new time period of the satellite will be:$ (1) $40 hours$ (2) $36 hours$ (3) $30 hours$ (4) $25 hours$ 174. $A man weighs Won the surface of the earth. What is his weight at a height equal to R? (R is Radius of earth)$ (1) $W$ (2) $W/2$ (3) $W/4$ (4) $W/8$ 175. $Consider a spherical planet which is rotating about its axis such that the speed of a point on its equator is v and the effective acceleration due to gravity on the equator is \frac{1}{3} of its value at the poles. What is the escape velocity for a particle at the pole of this planet.$ (1) $3 v$ (2) $2 v$ (3) $3 v$ (4) $2 v$ 176. $Two astronauts are floating in gravitational free space after having lost contact with their spaceship. The two will:$ (1) $keep floating at the same distance between them$ (2) $move towards each other$ (3) $move away from each other$ (4) $will become stationary$ 177. $A satellite of mass m is orbiting the earth (of radius R) at a height h from its surface. The total energy of the satellite in terms of g_{0}, the value of acceleration due to gravity at the earth's surface, is$ (1) $- \frac{2 m g _{0} R ^{2}}{R + h}$ (2) $\frac{m g _{0} R ^{2}}{2 ( R + h )}$ (3) $- \frac{m g _{0} R ^{2}}{2 ( R + h )}$ (4) $\frac{R m g _{0} R ^{2}}{R + h}$ 178. $The statements that are true about acceleration due to gravity, g (A) g is greater at poles.(B) g value decreases with height.(C) g value is same all over the earth.(D) g value is maximum at centre of earth.$ (1) $A and B$ (2) $A and D$ (3) $B and C$ (4) $C and D$ 179. $The mass of a spaceship is 800 kg . It is to be launched from the earth's surface out into free space. The value of g and R (radius of earth) are 10 m / s^{2} and 6400 km respectively. The required energy for this work will be$ (1) $6.4 \times 10^{8} Joule$ (2) $5.12 \times 10^{10} Joule$ (3) $6.4 \times 10^{9} Joule$ (4) $6.4 \times 10^{11} Joule$ 180. $The energy required to take a satellite to a height ’ h ’ above Earth surface (radius of Eareth = 6.4 \times 10^{3} km) is E_{1} and kinetic energy required for the satellite to be in a circular orbit at this height is E_{2} . The value of h for which E_{1} and E_{2} are equal, is:$ (1) $1.6 \times 10^{3} km$ (2) $3.2 \times 10^{3} km$ (3) $6.4 \times 10^{3} km$ (4) $28 \times 10^{4} km$