If g is the acceleration due to gravity on the earth’s surface, the gain in the potential energy of an abject…

Q: If g is the acceleration due to gravity on the earth’s surface, the gain in the potential energy of an abject of mass m raised from the surface of the earth to a height equal to the radius R of the earth, is

(a) (1/2) mgR

(b) 2 mgR

(c) mgR

(d) (1/4)mgR

Ans: (a)

Sol: Gain in the potential energy

$\large \Delta U = \frac{mgh}{1+\frac{h}{R}}$

Here , h = R

$\large \Delta U = \frac{1}{2}mgh$