First slide

Gravitaional potential energy

Question

A body is projected up from the surface of the earth with a velocity equal to 3/4^th of its escape velocity. If R be the radius of earth, the height it reaches is :

Moderate

A

3R/10
B

9R/7
C

8R/5
D

9R/5

Solution

By conservation of mechanical energy
$\begin{array}{l} - \frac{GMm}{R} + \frac{1}{2} m {(\frac{3}{4} \sqrt{\frac{2 GM}{R}})}^{2} = - \frac{GMm}{R + h} + 0 \\ \Rightarrow h = \frac{9}{7} R \end{array}$

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