Gravitation

A satellite of mass \(\mathrm{m}\) rotates round the earth in a circular orbit of radius R. If the angular momentum of the satellite is J, then its kinetic energy \((\mathrm{K})\) and the total energy (E) of the satellite are

An earth's satellite near the surface of the earth takes about 90 min per revolution. A satellite orbiting the moon also takes about \(90 \mathrm{~min}\) per revolution. Then which of the following is true?
[where \(\rho_{\mathrm{m}}\) is d...

Acceleration due to gravity at a height H from the surface of a planet is the same as that at a depth of H below the surface. If R be the radius of the planet, then H vs. R graph for different planets will be,

A body of mass m is thrown vertically upward with speed \(\sqrt3\) ve, where ve is the escape velocity of a body from earth surface. The final velocity of the body is

An ideal gas of molar mass M is contained in a very tall vertical cylindrical column in the uniform gravitational field. Assuming the gas temperature to be T, the height at which the centre of gravity of the gas is located is (R\(\to\)unive...

Assume that the earth moves around the sun in a circular orbit of radius R and there exists a planet which also move around the sun in a circular orbit with an angular speed twice as large as that of the earth. The earth of the orbit of the...

The ratio of accelerations due to gravity g1 : g2 on the surfaces of two planets is 5 : 2 and the ratio of their respective average densities \({{\rho _1}}\) : \({{\rho _2}}\) is 2 : 1. What is the ratio of respective escape velocities v1 :...

The weight of a body on surface of earth is 12.6 N. When it is raised to a height half the radius of earth, its weight will be

If the earth shrinks such that its mass does not change but radius decreases to one quarter of its original value then one complete day will take