Gravitation · Question 6

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

A body of mass 60 g experiences a gravitational force of 3.0 N, when placed at a particular point. The magnitude of the gravitational field intensity at that point is

1. 0.05 N/kg
2. 50 N/kg
3. 20 N/kg
4. 180 N/kg

Match List - I with List - II Choose the correct answer from the options given below

1. (a)-(ii), (b)-(i), (c)-(iv), (d)-(iii)
2. (a)-(ii), (b)-(iv), (c)-(i), (d)-(iii)
3. (a)-(ii), (b)-(iv), (c)-(iii), (d)-(i)
4. (a)-(iv), (b)-(ii), (c)-(i), (d)-(iii)

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