First slide

Gravitaional potential energy

Question

The magnitude of potential energy per unit mass of the object at the surface of earth is ‘E’. Then escape velocity of the object is

Easy

A

$\large \sqrt {2E}$
B

$\large 4{E^2}$
C

$\large \sqrt E$
D

$\large \sqrt {E/2}$

Solution

Potential energy per unit mass on the surface of earth = $\large -\frac{GM}{R}$
$\large \therefore E = \frac{GM}{R}$
Also , V_e = Escape velocity = $\large \sqrt{\frac{2GM}{R}}$
$\large \therefore V_e = \sqrt{2E}$

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