CBSE Class 11 Physics Gravitation Worksheet Set D

GRAVITATION

SECTION – A CONCEPTUAL AND APPLICATION TYPE QUESTIONS

Question. Taking the gravitational potential at a point infinte distance away as zero, the gravitational potential at a point A is –5 unit. If the gravitational potential at point infinite distance away is taken as + 10 units, the potential at point A is
(a) – 5 unit
(b) + 5 unit
(c) + 10 unit
(d) + 15 unit

Answer: B

Question. A man of mass m starts falling towards a planet of mass M and radius R. As he reaches near to the surface, he realizes that he will pass through a small hole in the planet. As he enters the hole, he sees that the planet is really made of two pieces a spherical shell of negligible thickness of mass 2M/ 3 and a point mass M/3 at the centre. Change in the force of gravity experienced by the man is
(a) 2/3 GMm/R²
(b) 0
(c) 1/3 GMm/R²
(d) 4/3 GMm/R²

Answer: A

Question. In a region of only gravitational field of mass 'M' a particle is shifted from A to B via three different paths in the figure. The work done in different paths are W₁, W₂, W₃ respectively then
(a) W₁ = W₂ = W₃
(b) W₁ > W₂ > W₃
(c) W₁ = W₂ > W₃
(d) W₁ < W₂ < W3

Answer: A

Question. Four similar particles of mass m are orbiting in a circle of radius r in the same angular direction because of their mutual gravitational attractive force. Velocity of a particle is given by 

Answer: A

Question. The time period of a satellite of earth is 5 hours. If the separation between the earth and the satellite is increased to 4 times the previous value, the new time period will become
(a) 10 hours
(b) 80 hours
(c) 40 hours
(d) 20 hours

Answer: C

Question. At sea level, a body will have minimum weight at
(a) pole
(b) equator
(c) 42° south latitude
(d) 37° north latitude

Answer: B

Question. The radius of the earth is 4 times that of the moon and its mass is 80 times that of the moon. If the acceleration due to gravity on the surface of the earth is 10 m/s², then on the surface of the moon its value will be
(a) 1 ms^–2
(b) 2 ms^–2
(c) 3 ms^–2
(d) 4 ms^–2

Answer: B

Question. A spherical uniform planet is rotating about its axis. The velocity of a point on its equator is V. Due to the rotation of planet about its axis the acceleration due to gravity g at equator is 1/2 of g at poles. The escape velocity of a particle on the pole of planet in terms of V is
(a) V_e = 2V
(b) V_e = V
(c) V_e = V/2
(d) V_e = √3V

Answer: A

Question. A planet of mass m moves around the sun of mass M in an elliptical orbit. The maximum and minimum distance of the planet from the sun are r₁ and r₂ respectively. The time period of planet is proportional to 

Answer: B

Question. The change in potential energy, when a body of mass m is raised to a height nR from the earth’s surface is (R = radius of earth) 

Answer: D

Question. A satellite is launched into a circular orbit of radius R around the earth. A second satellite is launched into an orbit of radius 1.01 R. The period of second satellite is larger than the first one by approximately
(a) 0.5%
(b) 1.0%
(c) 1.5%
(d) 3.0%

Answer: C

Question. The percentage change in the acceleration of the earth towards the sun from a total eclipse of the sun to the point where the moon is on a side of earth directly opposite to
the sun is 

Answer: C

Question. Imagine a new planet having the same density as that of earth but it is 3 times bigger than the earth in size. If the acceleration due to gravity on the surface of earth is g and that on the surface of the new planet is g’, then
(a) g’ = g/9
(b) g’ = 27g
(c) g’=9g
(d) g’=3g

Answer: D

Question. The orbital velocity of an artificial satellite in a circular orbit just above the centre’s surface is u. For a satellite orbiting at an altitude of half of the earth’s radius, the orbital velocity is 

Answer: A

Question. A diametrical tunnel is dug across the Earth. A ball is dropped into the tunnel from one side. The velocity of the ball when it reaches the centre of the Earth is .... (Given : gravitational potential at the centre of Earth =-3/2 GM/R)
(a) √R
(b) √gR
(c) √2.5gR
(d) √7.1gR

Answer: B

Question. Two identical geostationary satellites are moving with equal speeds in the same orbit but their sense of rotation brings them on a collision course. The debris will
(a) fall down
(b) move up
(c) begin to move from east to west in the same orbit
(d) begin to move from west to east in the same orbit

Answer: A

Question. At what height from the surface of earth the gravitational potential and the value of g are –5.4 × 10⁷ J kg^–1 and 6.0 ms^–2 respectively ?
Take the radius of earth as 6400 km : 
(a) 2600 km
(b) 1600 km
(c) 1400 km
(d) 2000 km

Answer: A

Question. A particle of mass M is situated at the centre of a spherical shell of same mass and radius a. The gravitational potential at a point situated at a/2 distance from the centre, will be
(a) -3GM/a
(b) -2GM/a
(c) -GM/a
(d) -4GM/a

Answer: A

Question. A planet moving along an elliptical orbit is closest to the sun at a distance r₁ and farthest away at a distance of r₂. If v₁ and v₂ are the linear velocities at these points respectively, then the ratio v₁/v₂ is 
(a) (r₁/r₂)²
(b) r₂/r₁
(c) (r₂/r₁)²
(d) r₁/r₂

Answer: B

Question. A particle of mass m is thrown upwards from the surface of the earth, with a velocity u. The mass and the radius of the earth are, respectively, M and R. G is gravitational constant and g is acceleration due to gravity on the surface of the earth. The minimum value of u so that the particle does not return back to earth, is
(a) √2GM/R
(b) √2GM/R²
(c) √2gR²
(d) √2GM/R²

Answer: A

Question. The earth is an approximate sphere. If the interior contained matter which is not of the same density everywhere, then on the surface of the earth, the acceleration due to gravity
(a) will be directed towards the centre but not the same everywhere
(b) will have the same value everywhere but not directed towards the centre
(c) will be same everywhere in magnitude directed towards the centre
(d) cannot be zero at any point

Answer: D

Question. For a satellite moving in an orbit around the earth, the ratio of kinetic energy to potential energy is
(a) 1/2
(b) 1/√2
(c) 2
(d) √2

Answer: A

Question. The figure shows elliptical orbit of a planet m about the sun S. The shaded area SCD is twice the shaded area SAB. If t₁ is the time for the planet to move from C to D and t₂ is the time to move from A to B then :
(a) t₁ = 4t₂
(b) t₁ = 2t₂
(c) t₁ = t₂
(d) t₁ > t₂

Answer: B

1. Why weight of a body becomes zero at the centre of earth ?

2. If the radius of earth becomes two times the present value and its mass remains unchanged , then how would the weight of an object on the surface of the earth would be affected ?

3. What is a parking orbit ?

4. Can a pendulum vibrate in an artificial satellite ?

5. The escape velocity of a body when projected from earth’s surface is 11.2 km/s. If it is projected at an angle of 50⁰ from the horizontal , what will be the escape velocity ?

6. If kinetic energy of a satellite revolving in an orbit close to the earth is doubled ,will the satellite escape?

7. Name two factors which determine whether a planet would have an atmosphere or not ?

8. Write two salient features of escape velocity ?

9. The gravitational potential energy of a body at a point in gravitational field of another body is –GMm/r . What does the negative sign indicate ?

10. Imagine a spacecraft going from the earth to the moon . How does its weight vary as it goes from the earth ?

11.What is Geosynchronous satellite ?

12. Two artificial satellites are revolving around the earth , one closer to its surface and the other away from it . Which has larger speed ?

13. State Kepler’s Laws of Planetary motion .

14.What is the value of gravitational potential energy at infinity ?

15. The moon has no atmosphere .Why ?

SECTION -B NUMERICAL QUESTIONS

Radius of earth R = 6400 km

1. Find the percentage decrease in weight of a body when taken to a height of 32km above the surface of earth , R = 6400 km.

2. How much below the surface of the earth does the acceleration due to gravity become 1 % of its value at earth’s surface ?

3. A body weighs 63 N on the surface of the earth. What is the gravitational force on it due to the earth at a height equal to half the radius of the earth ?

4. Find the potential energy of a system of a system of four particles each of mass m placed at vertices of a square of side L . Also calculate the potential at the centre of square .

5. The mass and diameter of a planet are twice those of the earth. What will be the period of oscillation of a pendulum on this planet, if it is a second’s pendulum on the earth?

6. To what height a mass can go , when sent up with a velocity half of the escape velocity from earth ? v_e= 11.2 km/s

7. Calculate the height of the orbit above the surface of the earth in which a satellite , if placed will appear stationary with respect t a particular place on earth .

8. An astronaut , on his journey between the earth and the moon experience weightlessness at a point P. Find the distance of the point P from the centre of the earth if the mass of earth is 80 times the mass of moon and the distance between them is 3.84 x 10 5 km.

9. A rocket is fired vertically from the surface of Mars with a speed of 2 km/ s . If 20 % of its initial energy is lost due to martial atmospheric resistance how far will the rocket go from the surface of Mars before returning to it ? Mass of Mars = 6.4 x 10 23kg , radius of Mars = 3400 km .

10. A mass of 20 kg is taken to a height of 160 km above the earth’s surface. Earth’s radius is about 6370 km .What is the mass of the object at that height ? How much does the object weigh at this height ?

11.Compare the period of revolution of a planet around the sun with that of the earth around the sun . The mean distance of the planet from the sun is 1.52 AU

12. The radii of two planets are R and 2R respectively and their densities are d and d/2 respectively . What is the ratio of acceleration due to gravity at their surfaces ?

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