Gravitation - Result Question 35
36. With what velocity should a particle be projected so that its height becomes equal to radius of earth?
[2001]
(a) $(\frac{G M}{R})^{1 / 2}$
(b) $(\frac{8 G M}{R})^{1 / 2}$
(c) $(\frac{2 G M}{R})^{1 / 2}$
(d) $(\frac{4 G M}{R})^{1 / 2}$
Topic 5: Motion of Satellites, Escape Speed and Orbital Velocity
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Answer:
Correct Answer: 36. (a)
Solution:
- (a) From conservation of energy
$ \begin{aligned} & \frac{1}{2} m u^{2}-\frac{G M m}{R}=\frac{1}{2} m \times(0)^{2}-\frac{G M m}{(R+R)} \\ & \Rightarrow u^{2}=\frac{2 G M}{R}-\frac{2 G M}{2 R}=\frac{G M}{R} \\ & \Rightarrow u=\sqrt{\frac{G M}{R}} \end{aligned} $
