Question

A body of mass m is situated at a distance $R _ { e }$ is the radius of earth. How much minimum energy be given to the body so that it may escape

• A. $m g R _ { e }$
• B. $2 m g R _ { e }$
• C. $\frac { m g R _ { e } } { 5 }$
• D. $\frac { m g R _ { e } } { 16 }$

Answer 1

Answer: (C)

$\frac { m g R _ { e } } { 5 }$

Answer 2

Potential energy of the body at a distance $4 R _ { e }$ from the surface of earth

$= - \frac { m g R _ { e } } { 1 + 4 } = - \frac { m g R _ { e } } { 5 }$

[As $h = 4 R _ { e }$ (given)]

So minimum energy required to escape the body will be $\frac { m g R _ { e } } { 5 }$.