Question

Two satellites are revolving round the earth at different heights. The ratio of their orbital speeds is $2:1$. If one of them is at a height of $100km$, the height of the other satellite is $($Radius of earth $R=6400$ km $)$

• A. 19600 km
• B. 24600 km
• C. 29600 km
• D. 14600 km

Answer 1

The correct option is A 19600 km

Orbital velocity is given by:
$V=\sqrt{\frac{GM}{R+h}}$
Where $G$ is the Universal Gravitational constant, $M$ is the mass of the Earth, $h$ is the height of the satellite from the earth's surface and $R$ is the radius of the earth.
$V\propto \frac{1}{\sqrt{R+h}}$
$\frac{V_1}{V_2}=\sqrt{\frac{R+h_2}{R+h_1}}$
Given: $\frac{V_1}{V_2}=\frac{2}{1}$, $h_1=100$ km and $R=6500$ $km$
$\Rightarrow \frac{2}{1}=\sqrt{\frac{6400+h_2}{6400+100}}$
$\Rightarrow 6400+h_2=4\times 6500=26000$ $km$
Hence, the height above the earth's surface, $h_2=26000-6400=19600$ $km$