$A$ particle is moving in a circular orbit of radius $r_1$ with an angular velocity $\omega_1$. It jumps to another circular orbit of radius $r_2$ and attains an angular velocity $\omega_2$. If $r_2 = 0.5\, r_1$ and assuming that no external torque is applied to the system,then the angular velocity $\omega_2$ is given by:

• A
  $\omega_2 = 4 \omega_1$
• B
  $\omega_2 = 3 \omega_1$
• C
  $\omega_2 = 2 \omega_1$
• D
  $\omega_2 = \omega_1$