Q154 / 225 · JEE Main 2002 · Physics

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

A
$\mathrm{mgR} / 2$
B
$2 \mathrm{mgR}$
Correct answer
C
$\mathrm{mgR}$
D
$\mathrm{mgR} / 4$

Solution

$\mathrm{KE}=\frac{1}{2} \mathrm{mv}_{\mathrm{esc}}^2=\frac{1}{2} \mathrm{~m}(\sqrt{2 \mathrm{gR}})^2=\mathrm{mgR}$

Hence, the correct answer is option: 'C'.

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