Gravitation

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

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