Gravitation

Correct formula for height of a satellite from earth's surface is :

1. ( T2R2g4 2 )1/3 - R
2. ( T2R2g4 )1/2 - R
3. ( T2R2g4 2 )-1/3 + R
4. ( T2R24 2g )1/3 - R

If R is the radius of the earth and the acceleration due to gravity on the surface of earth is g= 2 m/s2, then the length of the second's pendulum at a height h=2R from the surface of earth will be :

1. 19 m
2. 89 m
3. 29 m
4. 49 m

A light planet is revolving around a massive star in a circular orbit of radius R with a period of revolution T. If the force of attraction between planet and star is proportional to R-3/2 then choose the correct option :

1. T2 R7/2
2. T2 R3
3. T2 R5/2
4. T2 R3/2

Four identical particles of mass m are kept at the four corners of a square. If the gravitational force exerted on one of the masses by the other masses is ( 2 2+132 ) Gm2L2, the length of the sides of the square is

1. 4L
2. 3L
3. 2L
4. L2

The mass of the moon is 1144 times the mass of a planet and its diameter is 116 times the diameter of a planet. If the escape velocity on the planet is v, the escape velocity on the moon will be :

1. v4
2. v6
3. v12
4. v3

The gravitational potential at a point above the surface of earth is -5.12 107 J/kg and the acceleration due to gravity at that point is 6.4 m/s2. Assume that the mean radius of earth to be 6400 km. The height of this point above the earth's surface is :

1. 1600 km
2. 1200 km
3. 540 km
4. 1000 km

Escape velocity of a body from earth is 11.2 km/s. If the radius of a planet be one-third the radius of earth and mass be one-sixth that of earth, the escape velocity from the planet is :

1. 7.9 km/s
2. 8.4 km/s
3. 4.2 km/s
4. 11.2 km/s

At what distance above and below the surface of the earth a body will have same weight. (take radius of earth as R.)

1. 3R-R2
2. R2
3. 5R-R2
4. 5R-R

A planet takes 200 days to complete one revolution around the Sun. If the distance of the planet from Sun is reduced to one fourth of the original distance, how many days will it take to complete one revolution :

1. 20
2. 50
3. 100
4. 25

The acceleration due to gravity on the surface of earth is g. If the diameter of earth reduces to half of its original value and mass remains constant, then acceleration due to gravity on the surface of earth would be :

1. g/4
2. 2g
3. g/2
4. 4g