First slide

Gravitaional potential energy

Question

The earth is assumed to be a sphere of radius R. A platform is arranged at a height R from the surface of the earth. The escape velocity of a body from this platform is fv, where v is the escape velocity from the surface of the earth. The value of f is :

Moderate

A

$\sqrt{2}$
B

$\frac{1}{\sqrt{2}}$
C

$\frac{1}{3}$
D

$\frac{1}{2}$

Solution

By using conservation of mechanical energy
$- \frac{GMm}{(R + R)} + \frac{1}{2} m (fv)^{2} = 0 + 0$
Where $v = \sqrt{\frac{2 GM}{R}}$
$\Rightarrow f = \frac{1}{\sqrt{2}}$

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