An object is allowed to fall from a height R above earth, where R is radius of earth. Its velocity w

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7.Gravitation

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An object is allowed to fall from a height $R$ above the earth, where $R$ is the radius of earth. Its velocity when it strikes the earth's surface, ignoring air resistance, will be :

A

$2 \sqrt{g R}$

B

$\sqrt{g R}$

C

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

D

$\sqrt{2 g R}$

(JEE MAIN-2023)

Solution

Loss in $PE =$ Gain in $KE$

$\left(-\frac{ GMm }{2 R }\right)-\left(-\frac{ GMm }{ R }\right)=\frac{1}{2} mv ^2$

$\Rightarrow v ^2=\frac{ GM }{ R }= gR$

$\Rightarrow v =\sqrt{ gR }$

Standard 11

Physics

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