Question

If the gravitational force, between two masses, were to vary as 1/r³ , the work done in taking an object of mass m from the surface of the earth, to a height h (h is of the order of R), above the surface of the earth (radius of earth = R), would then be

(1) \(\frac{GMm}{2}[\frac{h(h+2R)}{R^2(R+h)^2}]\)

(2) \(\frac{GMm}{2}[\frac{R(h+2R)}{R^2(R+h)^2}]\)

(3) \(GMm[\frac{h(h+2R)}{R^2(R+h)^2}]\)

(4) \(GMm[\frac{h(h+2R)}{R^2(R+h)}]\)

Answer 1

 (1) \(\frac{GMm}{2}[\frac{h(h+2R)}{R^2(R+h)^2}]\)

The gravitational force, between the mass m and the earth (Mass = M), when the mass m is at a height x above the surface of the earth, would be

∴ The work done, in moving the object (against the gravitational force) from the surface of the earth to a height h above the surface, is