If the gravitational acceleration at the surface of earth is g, then increase in potential energy in lifting an object of mass m from earth surface to a height equal to half of radius of earth from surface will be:

At a point away from planet of radius 6400 km, the gravitational potential and field are –6.4 × 10⁷ SI units and 6.4 SI units respectively. Find height of that point above surface of planet.

Mass of moon is $\frac{1}{81}$  times the mass of a planet and radius is $\frac{1}{9}$  times the radius of the planet. The ratio of escape speed from planet to escape speed from moon is ________.

Gravitational force between two point masses is found to be F when both are in vacuum. If both the masses are immersed in water, new gravitational force will be:

Determine the energy required to launch a satellite of mass m from the surface of a planet of mass M and radius R in a circular orbit at an altitude of 3R.

Suppose the gravitational force varies inversely as the $n^{th}$  power of distance. Then, time period of a planet in circular orbit of radius R around the sum will be proportional to