Gravitation PYQs Set 1 (PDF)

Set 1 of 12 · Questions 1-30 of 351

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Mere Teacher · Previous Year Questions JEE Main Physics · Gravitation · Set 1 (Q1-30)
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1. $The minimum energy required to launch a satellite of mass m from the surface of earth of mass M and radius R in a circular orbit at an altitude of 2 R from the surface of the earth is: [NEET 2024]$ (1) $\frac{5 GmM}{6 R}$ (2) $\frac{2 GmM}{3 R}$ (3) $\frac{GmM}{2 R}$ (4) $\frac{GmM}{3 R}$ 2. $If the radius of earth shrinks by 2% while its mass remains same. The acceleration due to gravity on the earth's surface will approximately:$ (1) $decrease by 2%$ (2) $decrease by 4%$ (3) $increase by 2%$ (4) $increase by 4%$ 3. $The acceleration due to gravity on the earth's surface at the poles is g and angular velocity of the earth about the axis passing through the pole is ω . An object is weighed at the equator and at a height h above the poles by using a spring balance. If the weights are found to be same, then h is (h << R where R is the radius of the earth)$ (1) $\frac{R ^{2} ω ^{2}}{2 g}$ (2) $\frac{R ^{2} ω ^{2}}{g}$ (3) $\frac{R ^{2} ω ^{2}}{8 g}$ (4) $\frac{R ^{2} ω ^{2}}{4 g}$ 4. $If the mass of the Sun were ten times smaller and the universal gravitational constant were ten times larger in magnitude, which of the following is not correct?$ (1) $Raindrops will fall faster.$ (2) $'g' on the Earth will not change$ (3) $Time period of a simple pendulum on the Earth would decrease.$ (4) $Walking on the ground would become more difficult.$ 5. $A satellite is revolving in a circular orbit at a height h from the earth surface, such that h << R where R is the radius of the earth. Assuming that the effect of earth's atmosphere can be neglected the minimum increase in the speed required so that the satellite could escape from the gravitational field of earth is:$ (1) $2 gR$ (2) $gR$ (3) $\frac{gR}{2}$ (4) $gR (2 - 1)$ 6. $A body A of mass m is moving in a circular orbit of radius R about a planet. Another body B of mass \frac{m}{2} collides with A with a velocity which is half (\frac{v \to}{2}) the instantaneous velocity v \to of A . The collision is completely inelastic. Then, the combined body:$ (1) $Circular$ (2) $Elliptical$ (3) $Straight line$ (4) $Fall directly below on the ground$ 7. $The ratio of the weights of a body on the Earth's surface to that on the surface of a planet is 9 : 4 . The mass of the planet is \frac{1}{9} th of that of the Earth. If ’ R ’ is the radius of the Earth, what is the radius of the planet? (Take the planets to have the same mass density).$ (1) $\frac{R}{3}$ (2) $\frac{R}{4}$ (3) $\frac{R}{9}$ (4) $\frac{R}{2}$ 8. $Assume there are two identical simple pendulum Clocks-1 is placed on the earth and Clock-2 is placed on a space station located at a height h above the earth surface. Clock-1 and Clock-2 operate at time periods 4s and 6s respectively. Then the value of h is -(consider radius of earth R_{E} = 6400 km and g on earth 10m/ s^{2})$ (1) $1200 km$ (2) $1600km$ (3) $3200 km$ (4) $4800 km$ 9. $An astronaut takes a ball of mass m from earth to space. He throws the ball into a circular orbit about earth at an altitude of 318.5 km . From earth's surface to the orbit, the change in total mechanical energy of the ball is x \frac{GM _{m} m}{21 R _{e}} . The value of x is (take R_{e} = 6370 km):$ (1) $10$ (2) $12$ (3) $9$ (4) $11$ 10. $A mass m on the surface of the Earth is shifted to a target equal to the radius of the Earth. If R is the radius and M is the mass of the Earth, then work done in this process is$ (1) $\frac{m g R}{2}$ (2) $mgR$ (3) $2 mgR$ (4) $\frac{m g R}{4}$ 11. $Two stars of masses each, and at distance rotate in a plane about their common centre of mass . A meteorite passes through moving perpendicular to the star's rotation plane. In order to escape from the gravitational field of this double star, the minimum speed that meteorite should have at is:\n(Take Gravitational constant )$ (1) $2.4 \times 10^{4} m / s$ (2) $1.4 \times 10^{5} m / s$ (3) $3.8 \times 10^{4} m / s$ (4) $2.8 \times 10^{5} m / s$ 12. $The value of acceleration due to gravity at Earth's surface is 9.8 ms^{- 2} . The altitude above its surface at which theacceleration due to gravity decreases to 4.9 ms^{- 2} is close to: (Radius of earth = 6.4 \times 10^{6} m)$ (1) $2.6 \times 10^{6} m$ (2) $6.4 \times 10^{6} m$ (3) $9.0 \times 10^{6} m$ (4) $1.6 \times 10^{6} m$ 13. $The difference in the acceleration due to gravity at the pole and equator is (g = acceleration due to gravity, R = radius of earth, θ = latitude, ω = angular velocity, cos 0^{\circ} = 1, cos 90^{\circ} = 0)$ (1) $R ω^{2} g2$ (2) $ω cos^{2} θ$ (3) $R ω^{2}$ (4) $R ω^{2} cos^{2} θ$ 14. $Given radius of earth ‘R’ and length of a day ‘T’ the height of a geostationary satellite is [G - Gravitational constant, M - Mass of earth]$ (1) $(\frac{4 π ^{2} GM}{T ^{2}})^{1/3}$ (2) $(\frac{4 π GM}{R ^{2}})^{1/3} - R$ (3) $(\frac{GM T ^{2}}{4 π ^{2}})^{1/3} - R$ (4) $(\frac{GM T ^{2}}{4 π ^{2}})^{1/3} + R$ 15. $A light planet is revolving around a massive star in a circular orbit of radius R with a period of revolution T . If the force of attraction between planet and star is proportional to R^{- 3/2} then choose the correct option:$ (1) $T^{2} \propto R^{5/2}$ (2) $T^{2} \propto R^{7/2}$ (3) $T^{2} \propto R^{3/2}$ (4) $T^{2} \propto R^{3}$ 16. $The mass and the diameter of a planet are three times the respective values for the Earth. The period of oscillation of a simple pendulum on the Earth is 2 s. The period of oscillation of the same pendulum on the planet would be:$ (1) $\frac{3}{2} s$ (2) $\frac{2}{3} s$ (3) $\frac{3}{2} s$ (4) $23 s$ 17. $A body of mass is taken from earth surface to the height h equal to twice the radius of earth (R_{e}), the increase in potential energy will be: (g = acceleration due to gravity on the surface of Earth)$ (1) $3 m g R_{e}$ (2) $\frac{1}{3} m g R_{e}$ (3) $\frac{2}{3} m g R_{e}$ (4) $\frac{1}{2} m g R_{e}$ 18. $The mass of a planet is \frac{1}{10} th that of the earth and its diameter is half that of the earth. The acceleration due to gravity on that planet is: [NEET 2024]$ (1) $19.6 ms^{- 2}$ (2) $9.8 ms^{- 2}$ (3) $4.9 ms^{- 2}$ (4) $3.92 ms^{- 2}$ 19. $A geo-stationary satellite is orbiting the earth at a height of 6 R above the surface of the earth, R being the radius of the earth. The time period of another satellite at a height of 2.5 R from the surface of earth is -$ (1) $62 hr$ (2) $6 hr$ (3) $52 hr$ (4) $10 hr$ 20. $A body of mass 60 g experiences a gravitational force of 3.0 N, when placed at a particular point. The magnitude of the gravitational field intensity at that point is [NEET 2022]$ (1) $50 N / kg$ (2) $20 N / kg$ (3) $180 N / kg$ (4) $0.05 N / kg$ 21. $A body (mass m) starts its motion from rest from a point distant R_{0} (R_{0} > R) from the centre of the earth. The velocity acquired by the body when it reaches the surface of earth will be (G = universal constant of gravitation, M = mass of carth, R = radius of earth)$ (1) $2 GM (\frac{1}{R} - \frac{1}{R _{0}})$ (2) $(2 GM (\frac{1}{R} - \frac{1}{R _{0}}))^{\frac{1}{2}}$ (3) $GM (\frac{1}{R} - \frac{1}{R _{0}})$ (4) $2 GM ((\frac{1}{R} - \frac{1}{R _{0}}))^{\frac{1}{2}}$ 22. $The escape velocity from the earth's surface is v . The escape velocity from the surface of another planet having a radius, four times that of earth and same mass density is [NEET 2021]$ (1) $v$ (2) $2 v$ (3) $3 v$ (4) $4 v$ 23. $A geostationary satellite is taken to a new orbit, such that its distance from center of the earth is doubled. Then, find the time period of this satellite in the new orbit.$ (1) $24 h$ (2) $4.8 h$ (3) $482 h$ (4) $242 h$ 24. $Planet A has mass M and radius R . Planet B has half the mass and half the radius of Planet A . If the escape velocities from the Planets A and B are V_{A} and V_{B}, respectively, then v_{A} / v_{B} = n /4 . The value of n is:$ (1) $3$ (2) $2$ (3) $1$ (4) $4$ 25. $The vector form of universal law of gravitation$ (1) $F = G \frac{m _{1} m _{2}}{r} r$ (2) $F=Gm1m2r4r$ (3) $F = G \frac{m _{1} m _{2}}{r ^{2}} r$ (4) $F = G \frac{m _{1} m _{2}}{r ^{3}} r$ 26. $The mass of a spaceship is 1000 kg. It is to be launched from the earth's surface out into free space. The value of 'g' and 'R' (radius of earth) are 10 m/ s^{2} and 6400 km respectively. The required energy for this work will be:$ (1) $6.4 \times 1 0^{11} Joules$ (2) $6.4 \times 1 0^{8} Joules$ (3) $6.4 \times 1 0^{9} Joules$ (4) $6.4 \times 1 0^{10} Joules$ 27. $Two satellites A and B go around the earth in circular orbits at heights of R_{A} and R_{B} respectively from the surface of the earth. Assuming earth to be a uniform sphere of radius R_{e}, the ratio of the magnitudes of their orbital velocities is$ (1) $\frac{R _{B}}{R _{A}}$ (2) $\frac{R _{B} + R _{e}}{R _{A} + R _{e}}$ (3) $\frac{R _{B} + R _{e}}{R _{A} + R _{e}}$ (4) $\frac{R _{A}}{R _{B}}$ 28. $A 90 kg body placed at 2 R distance from surface of earth experiences gravitational pull of : (R = Radius of earth, g = 10 m s^{- 2})$ (1) $100 N$ (2) $300 N$ (3) $225 N$ (4) $120 N$ 29. $A planet is moving in an elliptical orbit around the sun. If T, V, E and L stand respectively for its kinetic energy, gravitational potential energy, total energy and magnitude of angular momentum about the centre of force, which of the following is correct?$ (1) $T is conserved$ (2) $V is always positive$ (3) $E is always negative$ (4) $L is conserved but direction of vector L changes continuously.$ 30. $Find the gravitational force between two stones, each of mass 2 kg and separated by a distance 1 m in vacuum.$ (1) $0$ (2) $6.675 \times 10^{- 5} N$ (3) $6.675 \times 10^{- 11} N$ (4) $2.67 \times 10^{- 10} N$