Question

If $v_0$ be the orbital velocity of an artificial satellite orbiting just above the earth's surface, then the orbital velocity of the same satellite orbiting at an altitude equal to earth's radius is

• A. $v_0\sqrt{\frac{2}{3}}$
• B. $v_0\sqrt{\frac{3}{2}}$
• C. $v_0\sqrt{2}$
• D. $\frac{v_0}{\sqrt{2}}$

Answer 1

Answer: (A)

$v_0\sqrt{\frac{2}{3}}$

$\frac{GMm}{R^2}=\frac{m{v}_0^2}{R}$--------------------$\left(1\right)$

$\frac{GMm}{\left(2R^2\right)}=\frac{m{v}^2}{2R}$--------------------$\left(2\right)$

$\Rightarrow \frac{GMm}{4R^2}=\frac{m{v}^2}{2R}$

$\Rightarrow v=\frac{v_0}{\sqrt{2}}$

Hence,

option $\left(D\right)$ is correct answer.