Gravitation PYQs Set 5 (PDF)

Set 5 of 12 · Questions 121-150 of 331

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Mere Teacher · Previous Year Questions NEET Physics · Gravitation · Set 5 (Q121-150)
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121. $A satellite is orbiting close to the earth and has a kinetic energy K . The minimum extra kinetic energy required by it to just overcome the gravitation pull of the earth is$ (1) $3 K$ (2) $K$ (3) $2 2 K$ (4) $2 K$ 122. $The acceleration due to gravity on the surface of earth is g . If the diameter of earth reduces to half of its original value and mass remains constant, then acceleration due to gravity on the surface of earth would be:$ (1) $g /4$ (2) $2 g$ (3) $g /2$ (4) $4 g$ 123. $Two astronauts are floating in gravitational free space after having lost contact with their spaceship. The two will [NEET 2017]$ (1) $keep floating at the same distance between them$ (2) $move towards each other$ (3) $move away from each other$ (4) $will become stationary$ 124. $The height ’ h ’ at which the weight of a body will be the same as that at the same depth ’ h ’ from the surface of the earth is (Radius of the earth is R and effect of the rotation of the earth is neglected)$ (1) $\frac{5 R - R}{2}$ (2) $\frac{3 R - R}{2}$ (3) $\frac{R}{2}$ (4) $\frac{5}{2} R - R$ 125. $When a planet revolves around the Sun, in general, for the planet$ (1) $linear momentum and linear velocity are constant.$ (2) $linear momentum and aerial velocity are constant.$ (3) $kinetic and potential energy of the planet are constant.$ (4) $angular momentum about the Sun and aerial velocity of the planet are constant.$ 126. $A satellite of mass m is orbiting the earth (of radius R) at a height h from its surface. The total energy of the satellite in terms of g_{0}, the value of acceleration due to gravity at the earth's surface is$ (1) $\frac{m g _{0} R ^{2}}{2 ( R + h )}$ (2) $- \frac{m g _{0} R ^{2}}{2 ( R + h )}$ (3) $\frac{2 m g _{0} R ^{2}}{R + h}$ (4) $- \frac{2 m g _{0} R ^{2}}{R + h}$ 127. $Let the escape speed of an object on the earth's surface be V_{0} . The object is projected out with speed 5 V_{0} . The speed of the object far away from the earth will be$ (1) $26 V_{0}$ (2) $4 V_{0}$ (3) $23 V_{0}$ (4) $32 V_{0}$ 128. $A spherical planet has a mass M_{P} and diameter D_{P} . A particle of mass m falling freely near the surface of this planet will experience an acceleration due to gravity, equal to:$ (1) $4 G M_{P} /D_{P}^{2}$ (2) $G M_{P} m/D_{P}^{2}$ (3) $G M_{P} /D_{P}^{2}$ (4) $4 G M_{P} m/D_{P}^{2}$ 129. $If the radius of the earth becomes x times its present value, the new period of rotation in hours is$ (1) $6 x^{2}$ (2) $12 x^{2}$ (3) $24 x^{2}$ (4) $48 x^{2}$ 130. $The maximum and minimum distances of a comet from the Sun are 1.6 \times 10^{12} m and 8.0 \times 10^{10} m respectively. If the speed of the comet at the nearest point is 6 \times 10^{4} ms^{- 1}, the speed at the farthest point is:$ (1) $1.5 \times 10^{3} m / s$ (2) $6.0 \times 10^{3} m / s$ (3) $3.0 \times 10^{3} m / s$ (4) $4.5 \times 10^{3} m / s$ 131. $Two satellites of mass m and 9 m are orbiting a planet in orbits of radius R . Their periods of revolution will be in the ratio of$ (1) $9 : 1$ (2) $3 : 1$ (3) $1 : 1$ (4) $1 : 3$ 132. $Two planets A and B of equal mass are having their period of revolutions T_{A} and T_{B} such that T_{A} = 2 T_{B} . These planets are revolving in the circular orbits of radii r_{A} and r_{B} respectively. Which out of the following would be the correct relationship of their orbits?$ (1) $2 r_{A}^{2} = r_{B}^{2}$ (2) $r_{A}^{3} = 2 r_{B}^{3}$ (3) $r_{A}^{3} = 4 r_{B}^{3}$ (4) $T_{A}^{2} - T_{B}^{2} = \frac{π ^{2}}{GM} (r_{B}^{3} - 4 r_{A}^{3})$ 133. $What is the depth at which the value of acceleration due to gravity becomes 1/ n times the value that the surface of Earth? (Radius of earth = R) [NEET 2020]$ (1) $R / n^{2}$ (2) $R (n - 1) / n$ (3) $Rn / (n - 1)$ (4) $R / n$ 134. $The mass density of a spherical galaxy varies as \frac{K}{r} over a large distance r' from its centre. In that region, a small star is in a circular orbit of radius R . Then the period of revolution, T depends on R as$ (1) $T^{2} \propto \frac{1}{R ^{3}}$ (2) $T^{2} \propto R$ (3) $T \propto R$ (4) $T^{2} \propto R^{3}$ 135. $The time period of a satellite of earth is 24 hours. If the separation between the earth and the satellite is decreased to one fourth of the previous value, then its new time period will become.$ (1) $4 hours$ (2) $6 hours$ (3) $12 hours$ (4) $3 hours$ 136. $A planet in a distant solar system is 10 times more massive than the earth and its radius is 10 times smaller. Given that the escape velocity from the earth is 11 km s^{-1}, the escape velocity from the surface of the planet would be:$ (1) $11 km s^{-1}$ (2) $110 km s^{-1}$ (3) $0.11 km s^{-1}$ (4) $1.1 km s^{-1}$ 137. $If the angular momentum of a planet of mass m, moving around the sun in a circular orbit is L, about the centre of the Sun, its areal velocity is:$ (1) $\frac{2 L}{m}$ (2) $\frac{4 L}{m}$ (3) $\frac{L}{2 m}$ (4) $\frac{L}{m}$ 138. $Starting from the center of the earth having radius R, the variation of g (acceleration due to gravity) is shown by [NEET 2016]$ (1) (2) (3) (4) 139. $A satellite revolving around the earth at a certain height experiences acceleration due to gravity equal to \frac{16}{49} g_{0}, where g_{0} is the acceleration due to gravity on the earth's surface. If R is the radius of earth, then the square of time period of the satellite's revolution is equal to K (\frac{π ^{2} R ^{3}}{GM}) . The value of K is$ (1) $\frac{27}{36}$ (2) $\frac{343}{16}$ (3) $\frac{125}{64}$ (4) $\frac{675}{81}$ 140. $Two satellites, A and B, have masses m and 2m respectively. A is in a circular orbit of radius R, and B is in a circular orbit of radius 2R around the earth. The ratio of their kinetic energies, \frac{T _{A}}{T _{B}}, is:$ (1) $1$ (2) $\frac{1}{2}$ (3) $2$ (4) $\frac{1}{2}$ 141. $A satellite of mass ' m' is revolving in a circular orbit of radius ' r' round the earth. Its angular momentum w.r.t. the centre of its orbit is (M = mass of earth, G = universal gravitational constant)$ (1) $(GMmr)^{1/2}$ (2) $(GM m^{2} r^{2})^{1/2}$ (3) $(GM m^{2} r)^{1/2}$ (4) $(G M^{2} m^{2} r)^{1/2}$ 142. $Initially a satellite of 100 kg is in a circular orbit of radius 1.5 R_{E} . This satellite can be moved to a circular orbit of radius 3 R_{E} by supplying α \times 10^{6} J of energy. The value of α is____. (Take Radius of Earth R_{E} = 6 \times 10^{6} m and g = 10 m / s^{2})$ (1) $150$ (2) $1000$ (3) $500$ (4) $100$ 143. $The value of acceleration due to gravity at a height of 4 R_{E} from surface of earth is (R_{E}) is radius of earth and acceleration due to gravity on the surface of the earth = (10 ms^{- 2})$ (1) $0.2 ms^{- 2}$ (2) $0.3 ms^{- 2}$ (3) $0.4 ms^{- 2}$ (4) $3 ms^{- 2}$ 144. $The depth d at which the value of acceleration due to gravity become \frac{1}{n} times the value at the earth's surface is (R = radius of earth)$ (1) $d = R (\frac{n}{n - 1})$ (2) $d = R (\frac{n - 1}{2 n})$ (3) $d = R (\frac{n - 1}{n})$ (4) $d = R^{2} (\frac{n - 1}{n})$ 145. $What is the minimum energy required to launch a satellite of mass m from the surface of a planet of mass M and radius R in a circular orbit at an altitude of 2R?$ (1) $\frac{5 GmM}{6 R}$ (2) $\frac{2 GmM}{3 R}$ (3) $\frac{GmM}{2 R}$ (4) $\frac{GmM}{3 R}$ 146. $A planet moving along an elliptical orbit is closest to the sun at a distance r_{1} and farthest away at a distance of r_{2} . If v_{1} and v_{2} are the linear velocities at these points respectively, then the ratio \frac{v _{1}}{v _{2}} is:$ (1) $(r_{1} / r_{2})^{2}$ (2) $r_{2} / r_{1}$ (3) $(r_{2} / r_{1})^{2}$ (4) $r_{1} / r_{2}$ 147. $A body weighs 300 N on the surface of the earth. How much will it weigh at a distance \frac{R}{2} below the surface of earth? (R \to Radius of earth)$ (1) $300 N$ (2) $250 N$ (3) $200 N$ (4) $150 N$ 148. $The acceleration due to gravity at a height 1 km above the earth is the same as at a depth d below the surface of earth. Then [NEET 2017]$ (1) $d = \frac{1}{2} km$ (2) $d = 1 km$ (3) $d = \frac{3}{2} km$ (4) $d = 2 km$ 149. $A test particle is moving in circular orbit in the gravitational field produced by a mass density r (r) = \frac{K}{r ^{2}} . Identify the correct relation between the radius R of the particle's orbit and its period T :$ (1) $T / R is a constant$ (2) $T^{2} / R^{3} is a constant$ (3) $T / R^{2} is a constant$ (4) $TR is a constant$ 150. $The mean radius of earth is R, its angular speed on its own axis is (f) and the acceleration due to gravity at earth’s surface is g . What will be the radius of the orbit of a geostationary satellite?$ (1) $(R^{2} g / ω^{2})^{1/3}$ (2) $(Rg / ω)^{2})^{1/3}$ (3) $(R^{2} ω^{2} / g)^{1/3}$ (4) $(R^{2} g / ω)^{1/3}$