Question

A body of mass m rises to height h = R/5 from the earth's surface, where R is earth's radius. If g is acceleration due to gravity at earth's surface, the increase in potential energy is

• A. mgh
• B. $\frac { 4 } { 5 } m g h$
• C. $\frac { 5 } { 6 } m g h$
• D. $\frac { 6 } { 7 } m g h$

Answer 1

Answer: (C)

$\frac { 5 } { 6 } m g h$

Answer 2

$\Delta U = \frac { m g h } { 1 + h / R }$

Substituting $R = 5 h$ we get $\Delta U = \frac { m g h } { 1 + 1 / 5 } = \frac { 5 } { 6 } m g h$