Question

The change in the gravitational potential energy when a body of mass m is raised to a height nR above the surface of the earth is (here, R is the radius of the earth)

• A. $\left(\frac{n}{n+1}\right)mgR$
• B. $\left(\frac{n}{n-1}\right)mgR$
• C. $nmgR$
• D. $\frac{mgR}{n}$

Answer 1

The correct option is A $\left(\frac{n}{n+1}\right)mgR$

Gravitational potential energy

$U_e=-\frac{GMm}{R}$

$U_h=\frac{GMm}{(R+nR)}=-\frac{GMm}{R(n+1)}$

$\Delta U=U_h-U_e$

$=\frac{GMm}{R}[1-\frac{1}{(n+1)}]$

$=\frac{n}{(n+1)}\left[\frac{GMm}{R}\right]$

$=\frac{n}{(n+1)}mgR$