First slide

Gravitaional potential energy

Question

If both the mass and the radius of earth decrease by 2%, the escape velocity from the surface of earth will

Easy

A

increase by 4%
B

decrease by 1.5%
C

increase by 1.5%
D

Remain unchanged

Solution

$V_{e} = {(\frac{2 G M}{R})}^{\frac{1}{2}}$
New mass $M^{1} = 0.98 M$ and New radius $R^{1} = 0.98 R$
$∴ V_{e}^{1} = \sqrt{\frac{2 G \times (0.98 M)}{(0.98 R)}} = \sqrt{\frac{2 G M}{R}} = V_{e}$

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