Question

The height from the surface of earth at which the gravitational potential energy of a ball of mass m is half of that at the centre of earth is (where R is radius of earth) :-

• A. $\frac{R}{4}$
• B. $\frac{R}{3}$
• C. $\frac{3R}{4}$
• D. $\frac{4R}{3}$

Answer 1

The correct option is B $\frac{R}{3}$

The gravitaional potential energy at center of earth is $\frac{3}{2}\frac{GMm}{R}$

( $\frac{3}{2}\frac{GMm}{R}$)$\frac{1}{2}$=$\frac{GMm}{x}$

$x=\frac{4R}{3}$

Height from surface of earth is $\frac{4R}{3}-R=\frac{R}{3}$