A particle of mass m is released from infinity and it move toward… - Vidyadip

MCQ

A particle of mass $m$ is released from infinity and it move towards a big solid sphere made of a jelly like material. Neglecting the resistance offered by material of sphere, find the velocity of the particle when it crosses the centre of the sphere

A
$\sqrt {\frac{{2GM}}{R}} $
B
$\sqrt {\frac{3}{2}\frac{{GM}}{R}} $
✓
$\sqrt {\frac{{3GM}}{R}} $
D
$\sqrt {\frac{{21GM}}{R}} $

✓

Answer

Correct option: C.

$\sqrt {\frac{{3GM}}{R}} $

c
$\frac{1}{2} \mathrm{mV}^{2}=\frac{3 \mathrm{GMm}}{2 \mathrm{R}} \Rightarrow \mathrm{V}=\sqrt{\frac{3 \mathrm{GM}}{\mathrm{R}}}$

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