Question

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

• A. $3R$
• B. $4R$
• C. $5R$
• D. $8R$

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
$\frac{1}{2}m\frac{5}{6}{V}_e^2+\left(\frac{-GMm}{R_e}\right)=\frac{1}{2}m{V}_0^2+\left(\frac{-GMm}{d}\right)$

$d=5R$