If G is the uciversal gravitational constant and p is the uniform density of a spherical planet. Then shortest possible period o0f rotation around a planet can be

The fastest possible rate of rotation of a planet is that for which the gravitational force on material at the equator just nearly provides the centripetal force needed for rotation. The corresponding shortest period of rotation is (If rho is the density of the earth)

A body on the equaotr of a planet weighs half of its weight at the pole. The density of matter of the planet is 3g//cm^(3) . Determine the peiod of rotation of the planet about its axis.

Prove that in the case of an artificial satellite revolving around a spherical planet, its minimum time period of revolution depends only on the mean density of the planet.

Consider a hypothetical planet which is very long and cylinderical. The density of the planet is rho , its radius is R . What is the possible orbital speed of the satellite in moving around the planet in circular orbit in a plane which is perpendicular to the axis of planet?

Consider a hypothetical planet which is very long and cylinderical. The density of the planet is rho , its radius is R . What is the possible orbital speed of the satellite in moving around the planet in circular orbit in a plane which is perpendicular to the axis of planet?

A planet is revolving around the sun. its distance from the sun at apogee is r_(A) and that at perigee is r_(p) . The masses of planet and sun are 'm' and M respectively, V_(A) is the velocity of planet at apogee and V_(P) is at perigee respectively and T is the time period of revolution of planet around the sun, then identify the wrong answer.

A planet is revolving around the sun. its distance from the sun at apogee is r_(A) and that at perigee is r_(p) . The masses of planet and sun are 'm' and M respectively, V_(A) is the velocity of planet at apogee and V_(P) is at perigee respectively and T is the time period of revolution of planet around the sun, then identify the wrong answer.