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 $$\left(\frac{2 \sqrt{2}+1}{32}\right) \frac{\mathrm{Gm}^2}{L^2}$$, the length of the sides of the square is

Escape velocity of a body from earth is $$11.2 \mathrm{~km} / \mathrm{s}$$. If the radius of a planet be onethird the radius of earth and mass be one-sixth that of earth, the escape velocity from the planet is :

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 :