Q138 / 150 · MHT CET 2009 · Physics

A particle of mass $m$ is rotating in a plane in circularpath of radius $r$. Its angular momentum is $L$. The centripetal force acting on the particle is

  • A
    $\frac{L^{2}}{m r}$
  • B
    $\frac{L^{2} m}{r}$
  • C
    $\frac{L^{2}}{m^{2} r^{2}}$
  • Correct answer
    D
    $\frac{L^{2}}{m r^{3}}$

Solution

Centripetal force, $F=\frac{m v^{2}}{r}=\frac{m}{r} \frac{L^{2}}{m^{2} r^{2}}=\frac{L^{2}}{m r^{3}}$ $\left[\right.$ As $\left.L=m v r \therefore v=\frac{L}{m r}\right]$

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

Relevant Questions