Question

A satellite projected with speed $\sqrt{\frac{5}{6}}$ times of its escape speed from earth's surface. The initial speed of satellite is parallel to the surface of earth . The maximum distance from the satellite centre of earth will be :

• A. $3R$
• B. $6R$
• C. $5R$
• D. None of these

Answer 1

Answer: (C)

$5R$

By angular momentum conservation,
$m\sqrt{\frac{5}{6}}{V}_{e}R=m{V}_{0}d$
and by energy conservation
$\frac{1}{2}m\frac{5}{6}{V}_e^2+\left(\frac{-GMm}{R_e}\right)=\frac{1}{2}m{V}_0^2+\left(\frac{-GMm}{d}\right)$

$⟹d=5R$