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 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 :

The escape velocity of a body depends upon mass as :

Energy required to move a body of mass m from an orbit of radius 2R to 3R is :

Average density of the earth:

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?

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

A planet of mass M is revolving round the sun of mass M_s in an elliptical orbit. The maximum and minimum distance of the planet from sun are r₁ and r₂ respectively. Then :

The weight of a body at earth surface is 700 g wt. What will be its weight on a planet whose mass is 1/7 that of earth and radius half that of earth?

The escape velocity for a body projected vertically upwards from the surface of earth is 11km/s. If the body is projected at an angle of 45° with the vertical, the escape velocity will be :