First slide

Gravitational potential and potential energy

Question

A rocket is launched from the surface of Earth with an initial speed of 10 kms^-1. The maximum distance of rocket from the surface of Earth is n $\times$ 10⁴ km. The value of n is __________.
(Radius of Earth = 6400 km and escape velocity from Earth's surface = 11.2 km/s) Neglect atmospheric resistance.

Difficult

Solution

$\begin{array}{l} - \frac{G M m}{R} + \frac{1}{2} m v^{2} = - \frac{G M m}{(R + h)} \\ \Rightarrow \frac{- G M}{R} + \frac{1}{2} v^{2} = \frac{- G M}{R + h} \\ \Rightarrow \frac{1}{2} v^{2} = \frac{- G M}{(R + h)} + \frac{G M}{R} \\ \Rightarrow \frac{1}{2} v^{2} = G M (- \frac{1}{R + h} + \frac{1}{R}) \end{array} \Rightarrow v^{2} = \frac{2 G M}{R} (1 - \frac{1}{1 + \frac{h}{R}}) h e r e, \frac{2 G M}{R} = {v_{e}}^{2} = {(11.2)}^{2} \Rightarrow {(\frac{10}{11.2})}^{2} = \frac{h}{R + h} \Rightarrow h = 2.58 \times 10^{4} k m$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App