Q87 / 120 · VITEEE 2009 · Physics

A body is projected vertically upwards from the surface of the earth with a velocity equal to half the escape velocity. If $R$ is the radius of the earth, maximum height attained by the body from the surface of the earth is

  • A
    $\frac{R}{6}$
  • Correct answer
    B
    $\frac{R}{3}$
  • C
    $\frac{2 R}{3}$
  • D
    $R$

Solution

Here, maximum height attained by a projectile $$ h=\frac{v^{2} R}{2 g R-v^{2}}...(i) $$ Velocity of body $=$ half the escape velocity i.e., $v=\frac{v_{e}}{2}$ or $v=\frac{\sqrt{2 g R}}{2} \Rightarrow v^{2}=\frac{2 g R}{4} \Rightarrow v^{2}=\left(\frac{g R}{2}\right)$ Now, putting value of $v^{2}$ in Eq. (i), we get Height, $h=\frac{\frac{g R}{2} \cdot R}{2 g R-\frac{g R}{2}}=\frac{\frac{g R^{2}}{2}}{\frac{3 g R}{2}}=\frac{R}{3}$

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

More Gravitation Questions