First slide

Gravitational potential and potential energy

Question

If mass of earth is M, radius is R and gravitational constant is G, then work done to take 1 kg mass from earth surface to infinity will be

Easy

A

$\sqrt{\frac{G M}{2 R}}$
B

$\frac{G M}{R}$
C

$\sqrt{\frac{2 G M}{R}}$
D

$\frac{G M}{2 R}$

Solution

Potential energy of the 1 kg mass which is placed at the earth surface = $- \frac{G M}{R}$
its potential energy at infinite = 0
$∴$ Work done = change in potential energy = $U_{f} - U_{i} = 0 - (\frac{- G m M}{R}) = \frac{G m M}{R} = \frac{G (1) M}{R} = = \frac{G M}{R}$

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