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?

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 :

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 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 :

The time period of an earth satellite in circular orbit is independent of :

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 :

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

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 escape velocity of a body depends upon mass as :

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 :