Question

The minimum energy required to launch a $m\text{kg}$ satellite from the earth’s surface in a circular orbit at an altitude $2R$, where $R$ is the radius of earth is

• A. $\frac{5}{3}mgR$
• B. $\frac{4}{3}mgR$
• C. $\frac{5}{6}mgR$
• D. $\frac{5}{4}mgR$

Answer 1

The correct option is C $\frac{5}{6}mgR$


Initial energy, $E_i=\frac{-GMm}{R}$
Final energy, $E_f=\frac{-GMm}{6R}$
Energy required , $\Delta E$ = $\frac{GMm}{R}-\frac{GMm}{6R}=\frac{-5GMm}{6R}$
As, $g=\frac{GM}{R^2}$
$\Delta E$ = $\frac{5g{R}^{2}m}{6R}=\frac{5gRm}{6}$