The gravitational potential at a point above the surface of earth is $$-5.12 \times 10^7 \mathrm{~J} / \mathrm{kg}$$ and the acceleration due to gravity at that point is $$6.4 \mathrm{~m} / \mathrm{s}^2$$. Assume that the mean radius of earth to be $$6400 \mathrm{~km}$$. The height of this point above the earth's surface is :

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 :

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

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : The angular speed of the moon in its orbit about the earth is more than the angular speed of the earth in its orbit about the sun.

Reason (R) : The moon takes less time to move around the earth than the time taken by the earth to move around the sun.

In the light of the above statements, choose the most appropriate answer from the options given below :