To project a body of mass m from earth's surface to infinity, required kinetic energy is (assume

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7.Gravitation

hard

To project a body of mass $m$ from earth's surface to infinity, the required kinetic energy is (assume, the radius of earth is $R_E, g=$ acceleration due to gravity on the surface of earth) :

A

$2 \mathrm{mgR}_{\mathrm{E}}$

B

$m g R_E$

C

$\frac{1}{2} \mathrm{mgR}_{\mathrm{E}}$

D

$4 \mathrm{mgR} R_E$

(JEE MAIN-2024)

Solution

$\frac{1}{2} \mathrm{mv}_{\mathrm{e}}^2=\frac{\mathrm{GMm}}{\mathrm{R}_{\mathrm{E}}}$

$\mathrm{g}=\frac{\mathrm{GM}}{\mathrm{R}_{\mathrm{E}}^2}$

$\mathrm{~K}=\mathrm{mgR}_{\mathrm{E}}$

Standard 11

Physics

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