BITSAT Physics Gravitation MCQs

Question: A body moves in a circular orbit of radius R under the action of a central force. Potential due to the central force is given by V(r) = kr (k is a positive constant). Period of revolution of the body is proportional to : 

• a) R^1/2
• b) R^–1/2
• c) R^–3/2 
• d) R^–5/2

Answer: R^1/2

Question: 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?

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: Kepler's third law states that square of period of revolution (T) of a planet around the sun, is proportional to third power of average distance r between sun and planet i.e. T² = Kr³ here K is constant. If the masses of sun and planet are M and m respectively then as per Newton's law of gravitation force of attraction between them is F

here G is gravitational constant. The relation between G and K is described as

• a) GMK = 4π²
• b) K = G
• c)

  

• d) GK = 4π²

Answer: GMK = 4π²

Question: What should be the velocity of rotation of earth due to rotation about its own axis so that the weight of a person becomes  of the present weight at the equator. Equatorial radius of the earth is 6400 km.

• a) 8.7 × 10^–7 rad/s
• b) 7.8 × 10^–4 rad/s
• c) 6.7 × 10^–4 rad/s
• d) 7.4 × 10^–3 rad/s

Answer: 7.8 × 10^–4 rad/s

Question: An artificial satellite is moving in a circular orbit around the earth with a speed equal to half the magnitude of the escape velocity from the earth. The height (h) of the satellite above the earth’s surface is (Take radius of earth as R_e) 

• a) h = R²_e
• b) h = R_e
• c) h = 2R_e
• d) h = 4R_e

Answer: h = R_e

Question: A spherically symmetric gravitational system of particles has a mass density   where ρ0 is a constant. A test mass can undergo circular motion under the influence of the gravitational field of particles. Its speed V as a function of distance r (0 < r < ∞) from the centre of the system is represented by

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: If the radius of the earth were to shrink by one per cent, its mass remaining the same, the value of g on the earth’s surface would

• a) increase by 0.5%
• b) increase by 2%
• c) Decrease by 0.5%
• d) Decrease by 2%.

Answer: increase by 2%

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)

  

• b) 0
• c)

  

• d)

  

Answer:

Question: Geo-stationary satellite is one which

• a) Remains stationary at a fixed height from the earth’s surface
• b) Revolves like other satellites but in the opposite direction of earth’s rotation
• c) Revolves round the earth at a suitable height with same angular velocity and in the same direction as earth does about its own axis
• d) None of these

Answer: Revolves round the earth at a suitable height with same angular velocity and in the same direction as earth does about its own axis

Question: Suppose the gravitational force varies inversely as the nth power of distance. Then the time period of a planet in circular orbit of radius ‘R’ around the sun will be proportional to

• a) Rⁿ
• b)

  

• c)

  

• d)

  

Answer:

Question: Two planets A and B have the same material density. If the radius of A is twice that of B, then the ratio of the escape velocity v_A/v_B is

• a) 2
• b)

  

• c)

  

• d) 1/2

Answer: 2

Question: The rotation of the earth having radius R about its axis speeds upto a value such that a man at latitude angle 60⁰ feels weightless. The duration of the day in such case will be :

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: The gravitational field in a region is given by  The change in the gravitational potential energy of a particle of mass 1 kg when it is taken from the origin to a point (7 m, – 3 m) is:

• a) 71 J
• b) 13√58J
• c) – 71 J
• d) 1 J

Answer: 1 J

Question: A particle released at a large distance from a planet reaches the planet only under gravitational attraction and passes through a smooth tunnel through its centre. If v_e is the escape velocity of a body at centre of the planet, then the particle’s speed at the centre of the planet is :

• a) v_e
• b) √1.5 v_e
• c) 1.5 v_e
• d) 2v_e

Answer: v_e

Question: A geostationary satellite is orbiting the earth at a height of 5R above that surface of the earth, R being the radius of the earth. The time period of another satellite in hours at a height of 2R from the surface of the earth is

• a) 5
• b) 10
• c) 6√2
• d) 6/ √2

Answer: 6√2

Question: The potential energy of a satellite of mass m and revolving at a height R_e above the surface of earth where R_e = radius of earth, is

• a) – m g R_e
• b)

  

• c)

  

• d)

  

Answer:

Question: Geo-stationary satellite is one which

• a) Remains stationary at a fixed height from the earth’s surface
• b) Revolves like other satellites but in the opposite direction of earth’s rotation
• c) Revolves round the earth at a suitable height with same angular velocity and in the same direction as earth does about its own axis
• d) None of these

Answer: Revolves round the earth at a suitable height with same angular velocity and in the same direction as earth does about its own axis

Question: Two planets A and B have the same material density. If the radius of A is twice that of B, then the ratio of the escape velocity v_A/v_B is

• a) 2
• b) 2
• c) 1/ √2
• d) 1/2

Answer: 2

Question: A geostationary satellite is orbiting the earth at a height of 5R above that surface of the earth, R being the radius of the earth. The time period of another satellite in hours at a height of 2R from the surface of the earth is

• a) 5
• b) 10
• c) 6 √2 
• d) 6/ √2

Answer: 6 √2 

Question: A particle released at a large distance from a planet reaches the planet only under gravitational attraction and passes through a smooth tunnel through its centre. If v_e is the escape velocity of a body at centre of the planet, then the particle’s speed at the centre of the planet is :

• a) v_e
• b) √1.5 v_e
• c) 1.5 v_e
• d) 2v_e

Answer: v_e