First slide

Motion of planets and satellites

Question

A body of mass m is situated at a distance 4R_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

Moderate

A

${mgR}_{e}$
B

$2 {mgR}_{e}$
C

$\frac{{mgR}_{e}}{5}$
D

$\frac{{mgR}_{e}}{16}$

Solution

Potential energy of the body at a distance 4R_e from the surface of earth
$U = - \frac{{mgR}_{e}}{1 + h / R_{e}} = - \frac{{mgR}_{e}}{1 + 4} = - \frac{{mgR}_{e}}{5}$
[As h = 4R_e (given)]
So minimum energy required to escape the body will be $\frac{{mgR}_{e}}{5}$ .

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