An artificial satellite is moving around earth in a circular orbi… - Vidyadip

MCQ

An artificial satellite is moving around earth in a circular orbit with speed equal to one fourth the escape speed of a body from the surface of earth. The height of satellite above earth's surface is ............ ($R$ is radius of earth)

A
$3 R$
B
$5 R$
✓
$7 R$
D
$8 R$

✓

Answer

Correct option: C.

$7 R$

c
(c)

Escape velocity $=\sqrt{2 gR }$

Speed of satellite $=\frac{\sqrt{2 g R}}{4}$

By force balance,

$\frac{ GMm }{ x ^2}=\frac{ m \left(\frac{\sqrt{2 gR }}{4}\right)^2}{ x }$

$x =\frac{ GM }{2 gR } \times 16=8 \frac{ GM }{ gR }=8 R$

Height of satellite above earth's surface is $8 R-R=7 R$

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