First slide

Gravitaional potential energy

Question

The kinetic energy needed to project a body of mass m from the earth's surface (radius R ) to infinity is

Moderate

A

$\frac{mgR}{2}$
B

2mgR
C

mgR
D

$\frac{mgR}{4}$

Solution

$- \frac{GMm}{R} + {(KE)}_{min} = 0 + 0 \Rightarrow {(KE)}_{\min} = \frac{GMm}{R} = m \frac{GM}{R^{2}} R = mgR$

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