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 $=\frac{GM}{R}=gR$