If' ‘g' is the acceleration due to gravity on the earth's surface, the gain in the 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

(a) ½ mgR

(b) ½ mgR

(c) 2 mgR

(d) mgR

(b) At earth surface, P.E. of system is – GmM/R At a distance R from the earth’s surface, P.E. of system is – GmM/2R

? ? U = - GmM / 2R + GmM/R ; ?U = GmM /2R

(b) At earth surface, P.E. of system is –GmM/R At a distance R from the earth’s surface, P.E. of system is – GmM/2R? ? U = - GmM / 2R + GmM/R ; ?U = GmM /2RNow GM/R2 = g; ?GM / R = gR ? ?U = ½ mgR