Physics Gravitation

Two stars of masses m and 2m at a distance d rotate about their common  centre of mass in free space. The

Four identical particles of equal masses 1kg made to move along the circumference of a circle of radius 1m under the actin of their own mutual gravitational attraction. The speed of each particle will be:

 Consider two satellites S₁ and S₂ with periods of revolution 1hr. and 8 hr. respectively revolving around a planet in circular orbits. The ratio of angular velocity of satellite S₁ to the angular velocity of satellites S₂ is:

The height of any point P above the surface of earth is equal to diameter of earth. The value of acceleration due to gravity at point P will be: (Given g = acceleration due to gravity at the surface of earth.

A particle of mass ' m ' is projected with a velocity v = kVe(k < 1) from the surface of the earth.
(Ve = escape velocity)
The maximum height above the surface reached by the particle is:
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A planet is revolving around the sun in an elliptical orbit. The mass of planet is m, angular momentum of planet about sun is L, and length of semi major axis is a and eccentricity is e. Time period of revolution of planet is given by

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 $\frac{3\pi }{\mathrm{G}\mathrm{d}}$  represents:
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Two bodies of mass m and 9m are placed at a distance <!-- [if gte msEquation 12]>R R<!--[endif]--><!--[endif]-->. The gravitational potential on the line joining the bodies where the gravitational field equals zero, will be ( G =  gravitational constant):
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The volume occupied by the molecules contained in 4.5Kg water at STP, if the intermolecular forces vanish away is :
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The escape velocity from the Earth's surface is $v$ . The escape velocity from the surface of another planet having a radius, four times that of Earth and same mass density is: