Gravitation

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

Two astronauts are floating in gravitational free space after having lost contact with their spaceship. The two will

1. move towards each other.
2. move away from each other.
3. will become stationary.
4. keep floating at the same distance between them.

At what height from the surface of earth the gravitation potential and the value of g are -5.4 107 J kg-1 and 6.0 m s-2 respectively? Take the radius of earth as 6400 km.

1. 1400 km
2. 2000 km
3. 2600 km
4. 1600 km

The ratio of escape velocity at earth (ve) to the escape velocity at a planet (vp) whose radius and mean density are twice as that of earth is

1. 1 : 4
2. 1 : 2
3. 1 : 2
4. 1 : 2 2

Starting from the centre of the earth having radius R, the variation of g (acceleration due to gravity) is shown by

1. [figure]
2. [figure]
3. [figure]
4. [figure]

A satellite of mass m is orbiting the earth (of radius R) at a height h from its surface. The total energy of the satellite in terms of g0, the value of acceleration due to gravity at the earth's surface, is

1. mg0R22(R+h)
2. - mg0R22(R+h)
3. 2mg0R2R+h
4. - 2mg0R2R+h

A remote-sensing satellite of earth revolves in a circular orbit at a height of 0.25 106 m above the surface of earth. If earth's radius is 6.38 106 m and g = 9.8 m s-2, then the orbital speed of the satellite is

1. 9.13 km s-1
2. 6.67 km s-1
3. 7.76 km s-1
4. 8.56 km s-1

A satellite S is moving in an elliptical orbit around the earth. The mass of the satellite is very small compared to the mass of the earth. Then,

1. the linear momentum of S remains constant in magnitude.
2. the acceleration of S is always directed towards the centre of the earth.
3. the angular momentum of S about the centre of the earth changes in direction, but its magnitude remains constant.
4. the total mechanical energy of S varies periodically with time.

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 = GMmr2, here G is gravitational constant. The relation between G and K is described as

1. K = G
2. K = 1G
3. GK = 4 2
4. GMK = 4 2