First slide

Gravitaional potential energy

Question

The escape velocity of a body on the earth’s surface is ve. A body is thrown up with a speed of kve, where k >1, Assuming that the sun and planets do not influence the motion of the body, then the velocity of the body at the infinite distance is

Moderate

A

$\large \frac {V_e} {\sqrt {k^2-1}}$
B

$\large {V_e} {\sqrt {k^2-1}}$
C

$\large {V_e} (k^2-1)$
D

$\large \frac {V_e}{k-1}$

Solution

$\large \frac{{ - GMm}}{R} + \frac{1} {2}m{K^2}V_e^2 = \frac{1} {2}m{V^2}$
$\large V_e^2 = \frac{{2GM}} {R} \Rightarrow \frac{{ - V_e^2}}{2} + \frac{1}{2} {K^2}V_e^2 = \frac{1} {2}{V^2}$
$\large {V^2} = V_e^2\left( {{K^2} - 1} \right) \Rightarrow V = {V_e}\sqrt {{K^2} - 1}$

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