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7.Gravitation
medium
A stationary object is released from a point $P$ at a distance $3 R$ 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?
A
$\left(\frac{2 G M}{3 R}\right)^{1 / 2}$
B
$\left(\frac{4 G M}{3 R}\right)^{1 / 2}$
C
$\left(\frac{G M}{3 R}\right)^{1 / 2}$
D
$\left(\frac{G M}{R}\right)^{1 / 2}$
Solution
(b)
Conserving mechanical energy between points $P$ and $S$,
$-\frac{G M m}{3 R}=\frac{1}{2} m v^2-\frac{G M m}{R}$
$\Rightarrow \frac{1}{2} m v^2=-\frac{G M m}{3 R}+\frac{G M m}{R}$
$=\frac{G M m}{R}\left(\frac{-1}{3}+1\right)$
$\frac{1}{2} \not m v^2=\frac{2 G M \not m}{3 R}$
$\Rightarrow v=\sqrt{\frac{4 G M}{3 R}}$
Standard 11
Physics
