The moment of inertia of a unifmm rod of mass M and length L about an axis through centre and perpendicular to length L is given by (`ML^(2))/12` . Now consider one such rod pivoted at its centre free to rotate in a vertical plane. The rod is at rest in the vertical position. A bullet of mass M moving horizontally at a speed V strikes and gets embedded in one end of the rod. The angular velocity CD of the rod after collision will be

Options

A. `V//L`
B. `2V//L`
C. `3V//2L`
D. `6V//L`

Answer

C

Explanation

Angular momentum conservation gives
`MVL/2=(ML^(2))/3omegarArromega=(3V)/(2L)`