Question

A rod of mass 'M' & length 'L' lying on a frictionless horizontal surface is initially given an angular velocity 'w' about vertical axis with centre of mass at rest but circular motion is not fixed. Subsequently end A of rod collides with nail P, which is near to A such that end A becomes stationary immediately after impact. Velocity of end 'B' just after collision will be –

• A. wL
• B. $\frac{\omega L}{2}$
• C. $\frac{\omega L}{4}$
• D. $\frac{7\omega L}{3}$

Answer 1

Answer: (C)

$\frac{\omega L}{4}$

Answer 2

Conservation of angular momentum about P

Ž $\frac{ML^{2}}{12}$ w = $\frac{ML^{2}}{3}$ w₁

Ž w₁ = $\frac{\omega}{4}$

V_B = $\frac{\omega L}{4}$