Question

A satellite is fired from the surface of the moon of mass $M$ and radius $R$ with speed $v_{0}at{30}^{\circ }$ with the vertical The satellite reaches a maximum distance of $\frac{5R}{2}$ from the center of the moon The value of $v_0$ is

• A. $\sqrt{\frac{2GM}{R}}$
• B. $\sqrt{\frac{5GM}{2R}}$
• C. $\sqrt{\frac{5GM}{4R}}$
• D. $\sqrt{\frac{2GM}{37R}}$

Answer 1

The correct option is C $\sqrt{\frac{5GM}{4R}}$

From conservation of angular momentum $m{v}_{0}R\sin {30}^{\circ }=mv\left(\frac{5R}{2}\right)\Rightarrow v_0=5v$

From conservation of mechanical energy - $\frac{GMm}{R}+\frac{1}{2}m{v}_0^2=-\frac{GMm}{5R/2}+\frac{1}{2}m{v}^2\Rightarrow v_0=\sqrt{\frac{5GM}{4R}}$