Gravitation - Result Question 49
52. The escape velocity of a sphere of mass $m$ is given by ( $G=$ Universal gravitational constant; $M=$ Mass of the earth and $R_e=$ Radius of the earth)
[1999]
(a) $\sqrt{\frac{G M}{R_e}}$
(b) $\sqrt{\frac{2 G M}{R_e}}$
(c) $\sqrt{\frac{2 G M m}{R_e}}$
(d) $\sqrt{\frac{2 G M+R_e}{R_e}}$
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Answer:
Correct Answer: 52. (b)
Solution:
- (b) Escape velocity is the minimum velocity with which a body is projected to escape from earth’s gravitational field
$\frac{1}{2} m v_e^{2}=\frac{G M m}{R_e} \Rightarrow v_e=\sqrt{\frac{2 G M}{R_e}}$
