Consider a rod of mass M and length L pivoted at its centre is 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 embedded in one end of the rod. The angular velocity of the rod just after the collision will be

Question

Consider a rod of mass M and length L pivoted at its centre is 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 embedded in one end of the rod. The angular velocity of the rod just after the collision will be (A) v/L (B) 2v/L (C) 3v/2L (D) 6v/L

Tardigrade Admin · Accepted Answer

Apply conservation of angular momentum about C. m v (L/2)=I ω, text where I=M((L/2))2+(M L2/12) ⇒ ω=(3 v/2 L)

v/L

2v/L

3v/2L

6v/L

Apply conservation of angular momentum about C. mv2L​=Iω, where I=M(2L​)2+12ML2​ ⇒ω=2L3v​

Apply conservation of angular momentum about $C$ .
$m v \frac{L}{2} = I ω, where I = M (\frac{L}{2})^{2} + \frac{M L ^{2}}{12}$
$\Rightarrow ω = \frac{3 v}{2 L}$