Q115 / 150 · MHT CET 2021 (20 Sep Shift 1) · Physics

A body is projected from earth's with thrice the escape velocity from the surface of the earth. What will be its velocity when it will escape the gravitational pull?

  • A
    $2 \mathrm{~V}_{\mathrm{e}}$
  • B
    $4 \mathrm{~V}_{\mathrm{e}}$
  • Correct answer
    C
    $2 \sqrt{2} \mathrm{~V}_{\mathrm{e}}$
  • D
    $\frac{V_e}{2}$

Solution

Energy required to escape the earth's gravitational field is $\frac{1}{2} \mathrm{mV}_e^2$ Energy given to the body is $=\frac{1}{2} \mathrm{~m}\left(3 \mathrm{~V}_{\mathrm{e}}\right)^2$ $=\frac{9}{2} \mathrm{mV}_{\mathrm{e}}^2$ $\therefore$ If $\mathrm{V}$ is velocity of the body when it has escaped from earth's gravitational field then $$ \begin{aligned} & \frac{1}{2} \mathrm{mV}^2=\frac{9}{2} \mathrm{mV}_{\mathrm{e}}^2-\frac{1}{2} \mathrm{mV}_{\mathrm{e}}^2 \\ & \therefore \frac{1}{2} \mathrm{mV}^2=4 \mathrm{mV}_{\mathrm{e}}^2 \\ & \therefore \mathrm{V}^2=8 \mathrm{~V}_{\mathrm{e}}^2 \\ & \mathrm{~V}=2 \sqrt{2} \mathrm{~V}_{\mathrm{e}} \end{aligned} $$

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

Relevant Questions