# A body of mass m is raised from the surface of the earth to a height nR ….

Q: A body of mass m  is raised from the surface of the earth to a height nR(R = radius of earth ). Magnitude of the change in the gravitational potential energy of the body is (g =acceleration due to gravity on the surface of earth)

(a) $\displaystyle (\frac{n}{n+1} ) mgR$

(b)$\displaystyle (\frac{n-1}{n} ) mgR$

(c) $\displaystyle \frac{mgR}{n}$

(d) $\displaystyle \frac{mgR}{n-1}$

Ans: (a)

Sol:
$\displaystyle U_1 = -\frac{G M m}{R}$

$\displaystyle U_2 = -\frac{G M m}{R+nR}$

$\displaystyle U_2 – U_1 = \frac{G M m}{R}(1-\frac{1}{n+1})$

$\displaystyle = \frac{G M m}{R} \frac{n}{n+1}$

$\displaystyle = \frac{g R^2 m}{R} \frac{n}{n+1}$

$\displaystyle = m g R \frac{n}{n+1}$