Gravitation · Question 13

A gravitational field is present in a region and a mass is shifted from A to B through different paths as shown. If W1, W2 and W3 represent the work done by the gravitational force along the respective paths, then : [figure]

1. W1 < W2 < W3
2. W1 = W2 = W3
3. W1 > W2 > W3
4. W1 > W3 > W2

In a gravitational field, the gravitational potential is given by, V = - Kx (J/Kg). The gravitational field intensity at point (2, 0, 3) m is

1. + K4
2. + K2
3. - K2
4. - K4

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 :

1. 4v
2. v
3. 2v
4. 3v

A particle of mass 'm' is projected with a velocity v = kVe (k < 1) from the surface of the earth. (Ve = escape velocity) The maximum height above the surface reached by the particle is :

1. Rk21-k2
2. R ( k1-k2 )2
3. R ( k1+k2 )2
4. R2k1+k

A body weighs 72 N on the surface of the earth. What is the gravitational force on it, at a height equal to half the radius of the earth?

1. 32 N
2. 30 N
3. 24 N
4. 48 N

The work done to raise a mass m from the surface of the earth to a height h, which is equal to the radius of the earth, is :

1. mgR
2. 2mgR
3. 12mgR
4. 32mgR

A body weighs 200 N on the surface of earth. How much will it weigh half way down to the centre of the earth?

1. 200 N
2. 250 N
3. 100 N
4. 150 N

The kinetic energies of a planet in an elliptical orbit about the Sun, at positions A, B and C are KA, KB and KC, respectively. AC is the major axis and SB is perpendicular to AC at the position of the Sun S as shown in the figure. Then [figure]

1. KA < KB < KC
2. KA > KB > KC
3. KB < KA < KC
4. KB > KA > KC

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. Walking on the ground would become more difficult.
3. Time period of a simple pendulum on the Earth would decrease.
4. g on the Earth will not change.

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

1. d = 1 km
2. d = 32 km
3. d = 2 km
4. d = 12 km