Gravitation - Result Question 40
43. A particle of mass ’ $m$ ’ is kept at rest at a height $3 R$ from the surface of earth, where ’ $R$ ’ is radius of earth and ’ $M$ ’ is mass of earth. The minimum speed with which it should be projected, so that it does not return back, is ( $g$ is acceleration due to gravity on the surface of earth)
[NEET Kar. 2013]
(a) $(\frac{G M}{R})^{\frac{1}{2}}$
(b) $(\frac{G M}{2 R})^{\frac{1}{2}}$
(c) $(\frac{g R}{4})^{\frac{1}{2}}$
(d) $(\frac{2 g}{4})^{\frac{1}{2}}$
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Answer:
Correct Answer: 43. (b)
Solution:
- (b) As we know, the minimum speed with which a body is projected so that it does not return back is called escape speed.
$V_e=\sqrt{\frac{2 G M}{r}}=\sqrt{\frac{2 G M}{R+h}}=\sqrt{\frac{2 G M}{4 R}}$
$ =(\frac{G M}{2 R})^{\frac{1}{2}}(\because h=3 R) $
