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

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?

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 :

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 :

The radius of earth is 6400 km and the value of g is 10m/s² . If the weight of 5km body on the equator becomes zero, then the angular speed of earth will be :

Suppose the gravitational force varies inversely as the n^th power of distance. Then the time period of a planet in circular orbit of radius R around the sun will be proportional to :

The time period of a satellite of earth is 5h. If the separation between the earth and the satellite is increased to 4 times the previous value, the new time period will become :

Average density of the earth:

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 :

A particle of mass 10g is kept on the surface of a uniform sphere of mass 100kg and radius 10cm. Find the work to be done against the gravitational force between them, to take the particle far away from the sphere :

(You may take G = 6.67 × 10^-11 Nm²/kg²)