Gravitation

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

A body of mass 'm' is taken from the earth's surface to the height equal to twice the radius (R) of the earth. The change in potential energy of body will be

1. 3mgR
2. 13mgR
3. mg2R
4. 23mgR

The radius of a planet is twice the radius of earth. Both have almost equal average mass densities. VP and VE are escape velocities of the planet and the earth, respectively, then

1. VP = 1.5 VE
2. VP = 2 VE
3. VE = 3 VP
4. VE = 1.5 VP

A particle of mass 'm' is kept at rest at a height 3R from the surface of earth, where 'R' is radius of earth and 'M' is mass of earth. The minimum speed with which it should be projected, so that it does not return back, is (g is acceleration due to gravity on the surface of earth)

1. ( GM2R )1/2
2. ( gR4 )1/2
3. ( 2gR )1/2
4. ( GMR )1/2

If ve is escape velocity and vo is orbital velocity of a satellite for orbit close to the earth's surface, then these are related by

1. vo = 2ve
2. vo = ve
3. ve = 2vo
4. ve = 2 vo