A body is released from a height equal to radius ( R ) of earth. velocity of body when it strikes su

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7.Gravitation

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A body is released from a height equal to the radius ( $R$ ) of the earth. The velocity of the body when it strikes the surface of the earth will be :

(Given $g$ = acceleration due to gravity on the earth.)

A

$\sqrt{g R}$

B

$\sqrt{4 g R}$

C

$\sqrt{2 g R}$

D

$\sqrt{\frac{g R}{2}}$

(JEE MAIN-2023)

Solution

By conservation of mechanical energy

$U _{ i }+ K _{ i }= U _{ f }+ K _{ i }$

$-\frac{ GMm }{2 R }+0=-\frac{ GMm }{ R }+\frac{1}{2} mv ^2$

$\frac{ GMm }{2 R }=\frac{1}{2} mv ^2$

$v =\sqrt{\frac{ GM }{ R }}=\sqrt{ gR }$

Standard 11

Physics

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