Gravitation Ques 43
43. A particle of mass $m$ is thrown upwards from the surface of the earth, with a velocity $u$. The mass and the radius of the earth are, respectively, $M$ and $R$. $G$ is gravitational constant and $g$ is acceleration due to gravity on the surface of the earth. The minimum value of $u$ so that the particle does not return back to earth, is
[2011 M]
(a) $\sqrt{\frac{2 GM}{R}}$
(b) $\sqrt{\frac{2 GM}{R^{2}}}$
(c) $\sqrt{2 gR^{2}}$
(d) $\sqrt{\frac{2 GM}{R^{2}}}$
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Answer:
Correct Answer: 43.(a)
Solution:
- (a) The velocity $u$ should be equal to the escape velocity. That is,
$u=\sqrt{2 gR}$
But $g=\frac{G M}{R^{2}}$
$\therefore u=\sqrt{2 \cdot \frac{GM}{R^{2}} \cdot R} \Rightarrow \sqrt{\frac{2 G M}{R}}$
BETA
