Q69 / 90 · JEE Main 2024 (06 Apr Shift 1) · Physics

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
    $2 m g R_E$
  • B
    $4 m g R_E$
  • Correct answer
    C
    $m g R_E$
  • D
    $1 / 2 m g R_E$

Solution

$\begin{aligned} & \frac{1}{2} \mathrm{mv}_{\mathrm{e}}^2=\frac{\mathrm{GMm}}{\mathrm{R}_{\mathrm{E}}} \\ & \mathrm{g}=\frac{\mathrm{GM}}{\mathrm{R}_{\mathrm{E}}^2} \\ & \mathrm{~K}=\mathrm{mgR}_{\mathrm{E}}\end{aligned}$

Hence, the correct answer is option: 'C'.

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