Question

The kinetic energy needed to project a body of mass $m$ from the earth's surface (radius $R$) to infinity is

• A. $\frac{1}{4}$ $mgR$
• B. $\frac{1}{2}$ $mgR$
• C. $mgR$
• D. $\frac{1}{3}$ $mgR$

Answer 1

The correct option is C $mgR$

Escape velocity ( in terms of radius of planet) is

$V_e=\sqrt{\frac{2GM}{R}}{V}_e=\sqrt{2gR}$
where $R$ is radius of earth
$\therefore$ Kinetic energy = $\frac{1}{2}mV{e}^2=\frac{1}{2}m\left(2gR\right)=mgR$