Gravitation · Question 1

Two planets P1 and P2 with equal mass have radii R1 and R2, respectively, where R2 = R12. The escape speeds of P1 and P2 are v1 and v2, respectively. Then v2v1 is:

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

In a solar system, the time-period of revolution of a planet tracing a circular orbit of radius R is proportional to:

1. R3
2. R1/2
3. R3/2
4. R2

The radius of Martian orbit around the Sun is about 4 times the radius of the orbit of Mercury. The Martian year is 687 Earth days. Then which of the following is the length of 1 year on Mercury?

1. 172 earth days
2. 124 earth days
3. 88 earth days
4. 225 earth days

A body weighs 48 N on the surface of the earth. The gravitational force experienced by the body due to the earth at a height equal to one-third the radius of the earth from its surface is:

1. 32 N
2. 36 N
3. 16 N
4. 27 N

The mass of a planet is 110th that of the earth and its diameter is half that of the earth. The acceleration due to gravity on that planet is:

1. 19.6 m s-2
2. 9.8 m s-2
3. 4.9 m s-2
4. 3.92 m s-2

The minimum energy required to launch a satellite of mass m from the surface of earth of mass M and radius R in a circular orbit at an altitude of 2R from the surface of the earth is:

1. 5GmM6R
2. 2GmM3R
3. GmM2R
4. GmM3R

The escape velocity for earth is v. A planet having 9 times mass that of earth and radius, 16 times that of earth, has the escape velocity of:

1. v3
2. 2v3
3. 3v4
4. 9v4

An object of mass 100 kg falls from point A to B as shown in figure. The change in its weight, corrected to the nearest integer is (RE is the radius of the earth) [figure]

1. 49 N
2. 89 N
3. 5 N
4. 10 N

Two bodies of mass m and 9m are placed at a distance R. The gravitational potential on the line joining the bodies where the gravitational field equals zero, will be (G = gravitational constant) :

1. - 12GmR
2. - 16GmR
3. - 20GmR
4. - 8GmR

A satellite is orbiting just above the surface of the earth with period T. If d is the density of the earth and G is the universal constant of gravitation, the quantity 3 Gd represents :

1. T2
2. T3
3. T
4. T