Question

When a satellite is moving around the earth with velocity v, then to make the satellite escape, the minimum percentage increase in its velocity should be [BHU 2012]

Easy

Solution

The orbital velocity of a satellite moving around the earth,
$v_{o} = \sqrt{g r}$
The escape velocity is given by $v_{e} = \sqrt{2 g r}$
$∴$ Increase in velocity $= \sqrt{2 g r} - \sqrt{g r}$
$= (\sqrt{2} - 1) \sqrt{g r} = 0.414 \sqrt{g r}$
So, percentage increase in velocity
$= \frac{0.414}{\sqrt{g r}} \sqrt{g r} \times 100 = 41.4 %$

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