Gravitation

AIPMT 2007MCQEasy📈 Topic in 12% papers+4−1

Ques. 1AIPMT 2007

Two satellites of earth, S1 and S2 are moving in the same orbit. The mass of S1 is four times the mass of S2. Which one of the following statements is true?

The potential energies of earth and satellite in the two cases are equal.
S1 and S2 are moving with the same speed.
The kinetic energies of the two satellites are equal.
The time period of S1 is four times that of S2.

Answer

(2) S1 and S2 are moving with the same speed.

Solution

Orbital speed: vo = GMr — independent of the satellite's mass ⇒ same for S1 and S2.

Time period: T = 2 rvo — also independent of mass ⇒ equal, so (4) is wrong.

PE = - GMmr and KE = GMm2r ∝ m ⇒ for S1 they are 4 times those of S2, so (1) and (3) are wrong.

Answer: (2)

Keep practising — Gravitation

Ques. 2AIPMT 2006

The earth is assumed to be a sphere of radius R. A platform is arranged at a height R from the surface of the earth. The escape velocity of a body from this platform is fv, where v is its escape velocity from the surface of the Earth. The value of f is

1/2
2
1/ 2
1/3

Ques. 3AIPMT 2005

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

g' = g/9
g' = 27g
g' = 9g
g' = 3g

Ques. 4AIPMT 2005

For a satellite moving in an orbit around the earth, the ratio of kinetic energy to potential energy is

1/2
1/ 2
2
2

Ques. 5AIPMT 2004

The density of a newly discovered planet is twice that of earth. The acceleration due to gravity at the surface of the planet is equal to that at the surface of the earth. If the radius of the earth is R, the radius of the planet would be

Ques. 6AIPMT 2003

Two spheres of masses m and M are situated in air and the gravitational force between them is F. The space around the masses is now filled with a liquid of specific gravity 3. The gravitational force will now be

Ques. 7AIPMT 2003

The acceleration due to gravity on the planet A is 9 times the acceleration due to gravity on planet B. A man jumps to a height of 2 m on the surface of A. What is the height of jump by the same person on the planet B?

(2/9) m
18 m
6 m
(2/3) m

Ques. 8AIPMT 2003

A body of mass m is placed on earth's surface which is taken from earth surface to a height of h = 3R, then change in gravitational potential energy is