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Standard XII

Physics

Escape Speed

A particle is...

Question

A particle is situated at a height $3 R$ from the earth surface. The velocity with which it should be projected vertically upward so that it does not return to earth is:

\sqrt{\frac{G M}{R}}

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\sqrt{\frac{2 G M}{R}}

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\sqrt{\frac{G M}{2 R}}

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\sqrt{\frac{G M}{4 R}}

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Solution

The correct option is A $\sqrt{\frac{G M}{2 R}}$
Conserving mechanical energy
$E_{i} = E_{f}$
$\frac{- G M m}{3 R + R} + \frac{1}{2} {m V}^{2} = 0 + 0$
$\Rightarrow \frac{G M}{4 R} = \frac{1}{2} V^{2}$
$\Rightarrow V = \sqrt{\frac{G M}{2 R}}$

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The correct option is A $\sqrt{\frac{G M}{2 R}}$
Conserving mechanical energy
$E_{i} = E_{f}$
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