Question

A body of mass m is situated at distance 4Rₑ above the earth's surface, where Rₑ is the radius of earth. How much minimum additional kinetic energy be given to the body so that it may escape?

• A. mgRₑ
• B. 2mgRₑ
• C. $\frac{mgRₑ}{5}$
• D. $\frac{mgRₑ}{16}$

Answer 1

Answer: (C)

$\frac{mgRₑ}{5}$

Answer 2

To escape Earth's gravity, the body's total energy must be at least zero at infinity. The initial potential energy at a distance $5R_e$ from Earth's center is $U_i = -\frac{GMm}{5R_e}$. Let $K_{add}$ be the minimum additional kinetic energy required. By conservation of energy, $U_i + K_{add} = 0$. Thus, $K_{add} = \frac{GMm}{5R_e}$. Using $GM = gR_e^2$, we get $K_{add} = \frac{mgR_e}{5}$.