Question

How much work per kilogram need to be done to shift a 1 kg mass from the surface of the earth to the infinity? (Take acceleration due to gravity = g, and radius of the earth = R)

• A. $ \frac{g}{R} $
• B. Rg
• C. $ g{{R}^{2}} $
• D. $ \frac{g}{{{R}^{2}}} $

Answer 1

Answer: (B)

Gravitational potential from the surface of earth to gravitational potential at $ \infty =0 $ Potential difference $ =-\,0-\left( -\frac{GM}{R} \right) $ $ \Delta V=\frac{GM}{R} $ Work done in shifting a body of mass m kg from the surface of earth to infinity. $ W=m\Delta V $ $ =\frac{GMm}{R} $ $ \therefore $ Work done per kg $ =\frac{GM}{R}=gR $