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  4. If the potential energy of a 3 kg body at the surface of a planet is -54 J, then its escape velocity (in m / s ) will be

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Q. If the potential energy of a $3 \,kg$ body at the surface of a planet is $-54 \,J$, then its escape velocity (in $m / s$ ) will be

Gravitation

Solution:

Gravitational potential energy $=\frac{-G M m}{R}$
$-54=\frac{-G M \times 3}{R}$
Hence, $\frac{G M}{R}=18$
But $v_{\text {esc }}=\sqrt{\frac{2 G M}{R}}=\sqrt{36}=6 \,m / s$