Two bodies of masses m and 4m are placed at a distance r. The gravitational potential at a point on the line joining them where the gravitational field is zero is:

If g is the acceleration due to gravity on the earth's surface, the gain in the potential energy of an object of mass m raised from the surface of the earth to a height equal to the radius R of the earth, is

From a solid sphere of mass M and radius R, a spherical portion of radius R/2 is removed, as shown in the figure Taking gravitational potential $V=0atr=\infty$, the potential at (G = gravitational constatn)

A mass $m$ is placed inside a hollow sphere of mass M as shown in figure. The gravitaional force on mass $m$ is

What would be the projections velocity of a satellite so that intersteller (interspace with no gravitation) velocity of the satellite becomes the orbital velocity when it is in the orbit at height of $10R$ from earth's surface, where $R$ is the radius of the earth?

Two point masses of mass $4m$ and $m$ respectively separated by $d$ distance are revolving under mutual force of attraction. Ration of their kinetic energies will be:

Two spherical bodies of mass M and 5M & radii R & 2R respectively are released in free space with initial separation between their centres equal to 12R. If they attract each other due to gravitational force only, then the distance covered by the smallar body just before collision is

The change in the value of 'g' at a height 'h' above the surface of the earth is the same as at a depth 'd' below the surface of earth. When both 'd' and 'h' are much smaller then the radius of earth, then which one of the following is correct?

The satellite of mass m revolving in a circular orbit of radius r around the earth has kinetic energy E. then, its angular momentum will be

Two particles of equal mass go around a circle of radius R under the action of their mutual gravitational attraction. Find the speed of each particle.