A body of mass m is situated at a distance 4Re above the earth’s surface, where Re is the radius of earth. How much minimum energy be given to the body so that it may escape

Question

A body of mass m is situated at a distance 4Re above the earth’s surface, where Re is the radius of earth. How much minimum energy be given to the body so that it may escape (A) mgRe (B) 2mgRe (C) (mgRe/5) (D) (mgRe/16)

Tardigrade Admin · Accepted Answer

Potential energy of the body at a distance

4 R_{e}

from the surface of earth

U = - \frac{m g R _{e}}{1 + h R _{e}} = - \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}

.

Q. A body of mass $m$ is situated at a distance $4 R_{e}$ above the earth’s surface, where $R_{e}$ is the radius of earth. How much minimum energy be given to the body so that it may escape

$m g R_{e}$

$2 m g R_{e}$

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

$\frac{m g R _{e}}{16}$

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

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

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

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

Q. A body of mass m is situated at a distance 4Re​ above the earth’s surface, where Re​ is the radius of earth. How much minimum energy be given to the body so that it may escape

mgRe​

2mgRe​

5mgRe​​

16mgRe​​