If g is the acceleration due to gravity on the earth's surface,the gain in 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 :

A planet in a distant solar system is 10 times more massive than the earth and its radius is 10 times smaller. Given that the escape velocity from the eath is 11kms^-1, the escape velocity from the surface of the planet would be :

An infinity number of point masses each equal to m are placed at x = 1, x = 2, x = 4, x = 8, ..... What is the total gravitational potential at x =0?

A satellite is revolving round the earth. Its K.E is E_k. How much would it be made so that the satellite may escape out of the gravitational field of earth?

Two spherical bodies of mass M and 5M and radii R and 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 smaller body just before collision is :

A satellite moves eastwards very near the surface of the earth in the equatorial plane of the earth with speed v₀. Another satellite moves at the same height with the same speed in the equatorial plane but westwards. If R is the radius of the earth and ω be its angular speed about its own axis, then the difference in the two time period as observed on the earth will be approximately equal to :

The kinetic energy needed to project a body of mass m from the earth's surface (radius R) to infinity is :

If suddenly the gravitational force of attraction between earth and a satellite revolving around it becomes zero, then the satellite will :

If the radius of the earth is made three times, keeping its mass constant, then the weight of a body on earth's surface will be as compared to its previous value :

g_e and g_p are accelerations due to gravity on the surface of earth and a planet respectively. The radius and mass of the planet are double the radius and mass of earth. Then :