First slide

Gravitaional potential energy

Question

A projectile is fired with a speed $v = 2 \sqrt{gR}$ from the surface of earth. It escapes the gravitational pull of earth. Its speed in interstellar space will be :

Moderate

A

$\sqrt{gR}$
B

$\sqrt{3 gR}$
C

$\sqrt{\frac{gR}{2}}$
D

$\sqrt{2 gR}$

Solution

$- \frac{GMm}{R} + \frac{1}{2} m (2 \sqrt{gR})^{2} = 0 + \frac{1}{2} {mv}_{\infty}^{2} \Rightarrow v_{\infty} = \sqrt{2 gR}$

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