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

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7.Gravitation

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

A

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

B

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

C

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

D

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

(AIPMT-2001)

Solution

$v^{2}=\frac{2 g h}{1+\frac{h}{R}}$

given $h=R$.

$v=\sqrt{g R}=\sqrt{\frac{G M}{R}} .$

Standard 11

Physics

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