With what velocity should a particle be projected so that its height becomes equal to radius of earth?

{(\frac{G M}{R})}^{1 / 2}

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{(\frac{8 G M}{R})}^{1 / 2}

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{(\frac{2 G M}{R})}^{1 / 2}

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{(\frac{4 G M}{R})}^{1 / 2}

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Solution

The correct option is A ${(\frac{G M}{R})}^{1 / 2}$
Let the particle is thrown with velocity $^{'} u^{'}$
Now,
on conserving mechanical energy.
$\frac{- G M m}{2 R} + 0 = 0 + \frac{1}{2} {m u}^{2}$
$u = \sqrt{\frac{G M}{R}}$

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With what velocity should a particle be projected so that its height becomes equal to radius of earth?

The correct option is A (GMR)1/2Let the particle is thrown with velocity ′u′Now, on conserving mechanical energy.−GMm2R+0=0+12mu2 u=√GMR

The correct option is A ${(\frac{G M}{R})}^{1 / 2}$
Let the particle is thrown with velocity $^{'} u^{'}$
Now,
on conserving mechanical energy.
$\frac{- G M m}{2 R} + 0 = 0 + \frac{1}{2} {m u}^{2}$
$u = \sqrt{\frac{G M}{R}}$