Gravitation

Given below are two statements : In the light of the above statements, choose the correct answer from the options given below :

1. Statement I is true but Statement II is false
2. Statement I is false but Statement II is true
3. Both Statement I and Statement II are true
4. Both Statement I and Statement II are false

Initially a satellite of 100 kg is in a circular orbit of radius 1.5RE. This satellite can be moved to a circular orbit of radius 3RE by supplying 106 J of energy. The value of is . (Take Radius of Earth RE = 6 106 m and g = 10 m/s2)

1. 500
2. 1000
3. 100
4. 150

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). In the light of the above statements, choose the most appropriate answer from the options given below:

1. (A) is not correct but (R) is correct
2. Both (A) and (R) are correct but (R) is not the correct explanation of (A)
3. Both (A) and (R) are correct and (R) is the correct explanation of (A)
4. (A) is correct but (R) is not correct

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R In the light of the above statements, choose the correct answer from the options given below

1. A is false but R is true
2. Both A and R are true and R is the correct explanation of A
3. A is true but R is false
4. Both A and R are true but R is NOT the correct explanation of A

An object is kept at rest at a distance of 3R above the earth's surface where R is earth's radius. The minimum speed with which it must be projected so that it does not return to earth is : (Assume M = mass of earth, G = Universal gravitational constant)

1. 3GMR
2. 2GMR
3. GM2R
4. GMR

Three identical spheres of mass m are placed at the vertices of an equilateral triangle of length a. When released, they interact only through gravitational force and collide after a time T = 4 seconds. If the sides of the triangle are increased to length 2a and also the masses of the spheres are made 2 m, then they will collide after seconds.

A satellite of mass 1000 kg is launched to revolve around the earth in an orbit at a height of 270 km from the earth's surface. Kinetic energy of the satellite in this orbit is 1010 J. (Mass of earth = 6 1024 kg, Radius of earth = 6.4 106 m, Gravitational constant = 6.67 10-11 N m2 kg-2)

Two planets, A and B are orbiting a common star in circular orbits of radii RA and RB, respectively, with RB=2RA. The planet B is 4 2 times more massive than planet A. The ratio ( LBLA ) of angular momentum (LB) of planet B to that of planet A (LA) is closest to integer .

Earth has mass 8 times and radius 2 times that of a planet. If the escape velocity from the earth is 11.2 km/s, the escape velocity in km/s from the planet will be:

1. 8.4
2. 11.2
3. 5.6
4. 2.8

A satellite is launched into a circular orbit of radius 'R' around the earth. A second satellite is launched into an orbit of radius 1.03 R. The time period of revolution of the second satellite is larger than the first one approximately by

1. 3%
2. 2.5%
3. 4.5%
4. 9%