Question

Consider the satellites revolving round the earth at different heights.The ratio of their orbital speed is 3 : 2 .If one of them is at a height of 200 Km, the height of the other satellite is (Radius of the earth is R=6400 Km)

• A. $8450Km$
• B. $845Km$
• C. $84.5Km$
• D. $84500Km$

Answer 1

Answer: (A)

$8450Km$

Orbital velocity $V_o=\sqrt{\frac{GM}{R+h}}$
Given : $\frac{V_o^{\prime }}{V_o}=\frac{3}{2}$
$\therefore$ $\sqrt{\frac{R+h}{R+h^{\prime }}}=\frac{3}{2}$
Or $\frac{R+h}{R+h^{\prime }}=\frac{9}{4}$
where $R=6400km$ and $h^{\prime }=200km$
$\therefore$ $\frac{6400+h}{6400+200}=\frac{9}{4}$
$⟹h=8450km$