A particle moves in a circular orbit of radius r under a central attractive force F = $-\frac{k}{r},$  k is constant. The time period of its motion is proportional to

A wire can be broken by a load of 20 kg-wt. The force required to break wire of same material with twice the diameter will be

The radii of circular orbits of two satellites A and B of the earth, are 4R and R, respectively. If speed of satellite A is 2V, then the speed of satellite B will be

At a point away from planet of radius 6400 km, the gravitational potential and field are –6.4 × 10⁷ SI units and 6.4 SI units respectively. Find height of that point above surface of planet.

Mass of moon is $\frac{1}{81}$  times the mass of a planet and radius is $\frac{1}{9}$  times the radius of the planet. The ratio of escape speed from planet to escape speed from moon is ________.

If the gravitational acceleration at the surface of earth is g, then increase in potential energy in lifting an object of mass m from earth surface to a height equal to half of radius of earth from surface will be: