Question

Abody of mass m is raised through a distance equal to the radius of the earth, (R), from the earth surface. Increase in potential energy is

• A. $mgR$
• B. $2 mgR$
• C. $\frac{mgR}{2}$
• D. $3 mgR$

Answer 1

Answer: (C)

$\frac{mgR}{2}$

Answer 2

Potential energy of mass $m$ on the surface of the earth, $U_1 = -mgR$.
Potential energy of mass $m$ at a distance $R$ above the surface of the earth, $U_1= -mg'(2R)$
Here, $g' = \frac{GM}{\left(R +R\right)^{2}} = \frac{g}{4}$
$\therefore\:\: U_{f} =-\frac{mgR}{2}$
Increase in potential energy of mass, m
$=U_{f} - U_{i} = - \frac{mgR}{2}+ mgR = mgR 2$