An artificial satellite is placed into a circular orbit around ea… - Vidyadip

MCQ

An artificial satellite is placed into a circular orbit around earth at such a height that it always remains above a definite place on the surface of earth. Its height from the surface of earth is ........... $km$

A
$6400$
B
$4800$
C
$32000$
✓
$36000$

✓

Answer

Correct option: D.

$36000$

d
As the satellite always remains stationary $w.r.t$ earth surface, thus its time period revolution is equal to time period of rotation of earth i.e $24\, hrs$

Time period of satellite $T=2 \pi \sqrt{\frac{r^{3}}{g R^{2}}}$ where $R=6400 \mathrm{km}=6.4 \times 10^{6} \mathrm{m}$

$\therefore 24 \times 3600=2 \pi \sqrt{\frac{r^{3}}{9.8\left(6.4 \times 10^{6}\right)^{2}}}$

OR $\frac{r^{3}}{401.408 \times 10^{12}}=1.89 \times 10^{8} \quad \Longrightarrow r^{3}=76 \times 10^{21}$

$\Rightarrow r=42400 \mathrm{km}$

Thus height of satellite above earth surface $\quad h=42400-6400=36000 \mathrm{km}$

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