Question

If $V_e$ is the escape velocity of a body from a planet of mass M and radius R. Then the velocity of the satellite revolving at height h from the surface of the planet will be:

• A. $V_e\sqrt{\frac{R}{R+h}}$
• B. $V_e\sqrt{\frac{2R}{R+h}}$
• C. $V_e\sqrt{\frac{R+h}{R}}$
• D. $V_e\sqrt{\frac{R}{2(R+h)}}$

Answer 1

The correct option is D $V_e\sqrt{\frac{R}{2(R+h)}}$

Escape velocity, $v_e=\sqrt{\frac{2G{M}_e}{R}}$

and orbital velocity, $v_o=\sqrt{\frac{G{M}_e}{(R+h)}}$

On dividing both equations, $v_o=v_e\sqrt{\frac{R}{2(R+h)}}$