Gravitation

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

Two spherical bodies of mass M and 5M and radii R and 2R are released in free space with initial separation between their centres equal to 12R. If they attract each other due to gravitational force only, then the distance covered by the smaller body before collision is :

1. 7.5R
2. 1.5R
3. 2.5R
4. 4.5R

A black hole is an object whose gravitational field is so strong that even light cannot escape from it. To what approximate radius would earth (mass = 5.98 1024 kg) have to be compressed to be a black hole?

1. 10-9 m
2. 10-6 m
3. 10-2 m
4. 100 m

Dependence of intensity of gravitational field (E) of earth with distance (r) from centre of earth is correctly represented by

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

Infinite number of bodies, each of mass 2 kg are situated on x-axis at distance 1 m, 2 m, 4 m, 8 m, . . . , respectively, from the origin. The resulting gravitational potential due to this system at the origin will be

1. - 43 G
2. - 4G
3. - G
4. - 83 G