Question

How much energy will be necessary for making a body of $500\, kg$ escape from the earth? $\left[ g =9.8 \,ms ^{2}\right.$, radius of the earth $\left.6.4 \times 10^{6} m \right]$

• A. About $ 9.8\times 10^{6}J $
• B. About $ 6.4\times 10^{8}J $
• C. About $ 3.1\times 10^{10}J $
• D. About $ 27.4\times 10^{12}J $

Answer 1

Answer: (C)

Escape velocity $v_{e}=\sqrt{2 g R}$
Kinetic energy of the body required to escape
$K E=\frac{1}{2} m v_{e}^{2}$
or $K E=\frac{1}{2} m(2 g R)$
or $K E=m g R$
or $K E=500 \times 9.8 \times 6.4 \times 10^{6} $
$\Rightarrow K E=3.1 \times 10^{10} J$