A stationary object is released from a point | vedclass

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Question

(B) By applying the principle of conservation of mechanical energy between the initial point $P$ (at distance $3R$ from the center) and the surface of

Vedclass · Accepted Answer

$\left(\frac{4 G M}{3 R}\right)^{1 / 2}$

Vedclass · Answer

(B) By applying the principle of conservation of mechanical energy between the initial point $P$ (at distance $3R$ from the center) and the surface of the moon $S$ (at distance $R$ from the center):Initial Mechanical Energy $(E_i)$ = Final Mechanical Energy $(E_f)$$E_i = K_i + U_i = 0 + \left(-\frac{G M m}{3 R}\right) = -\frac{G M m}{3 R}$$E_f = K_f + U_f = \frac{1}{2} m v^2 + \left(-\frac{G M m}{R}\right)$Equating $E_i$ and $E_f$:$-\frac{G M m}{3 R} = \frac{1}{2} m v^2 - \frac{G M m}{R}$$\frac{1}{2} m v^2 = \frac{G M m}{R} - \frac{G M m}{3 R}$$\frac{1}{2} m v^2 = \frac{G M m}{R} \left(1 - \frac{1}{3}\right) = \frac{G M m}{R} \left(\frac{2}{3}\right)$$\frac{1}{2} v^2 = \frac{2 G M}{3 R}$$v^2 = \frac{4 G M}{3 R}$$v = \sqrt{\frac{4 G M}{3 R}}$Thus,the correct option is $(B)$.

$A$ stationary object is released from a point $P$ at a distance $3R$ from the centre of the moon,which has radius $R$ and mass $M$. Which of the following gives the speed of the object on hitting the moon?

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