The escape velocity of a body on the earth surface is $$11.2 \mathrm{~km} / \mathrm{s}$$. If the same body is projected upward with velocity $$22.4 \mathrm{~km} / \mathrm{s}$$, the velocity of this body at infinite distance from the centre of the earth will be:
If $$\mathrm{R}$$ is the radius of the earth and $$\mathrm{g}$$ is the acceleration due to gravity on the earth surface. Then the mean density of the earth will be :
Two bodies of mass $$m$$ and $$9 m$$ are placed at a distance $$R$$. The gravitational potential on the line joining the bodies where the gravitational field equals zero, will be ($$G=$$ gravitational constant) :
A satellite is orbiting just above the surface of the earth with period $$T$$. If $$d$$ is the density of the earth and $$G$$ is the universal constant of gravitation, the quantity $$\frac{3 \pi}{G d}$$ represents :