First slide

Gravitaional potential energy

Question

The work done to raise a mass m from the surface of the earth to a height h, which is equal to the radius of the earth, is

Easy

A

$\frac{3}{2} mgR$
B

$m g R$
C

$2 mgR$
D

$\frac{1}{2} mgR$

Solution

Work done =Change in potential energy
$= U_{f} - U_{i} = \frac{- GMm}{(R + h)} - (\frac{- GMm}{R})$
where M is the mass of earth and R is the radius of earth.
$∴ W = GMm [\frac{1}{R} - \frac{1}{(R + h)}] Now, h = R ∴ W = GMm [\frac{1}{R} - \frac{1}{2 R}] = \frac{GMm}{2 R} \Rightarrow W = \frac{mgR}{2} [∵ g = \frac{GM}{R^{2}}]$

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