A rod of length L and mass M is hinged at point O. A small bullet of mass m hits the rod as shown in the figure. The bullet gets embedded in the rod. Find angular velocity of the system just after impact.

Question

A rod of length L and mass M is hinged at point O. A small bullet of mass m hits the rod as shown in the figure. The bullet gets embedded in the rod. Find angular velocity of the system just after impact. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Angular momentum of the system about an axis perpendicular to plane of paper and passing through O will remain conserved. Li=Lf ∴ mvL=Iω=(mL2+(ML2/3))ω ∴ ω=(3mv/L(3m+M))

Q. A rod of length L and mass M is hinged at point O. A small bullet of mass m hits the rod as shown in the figure. The bullet gets embedded in the rod. Find angular velocity of the system just after impact.

Angular momentum of the system about an axis perpendicular to plane of paper and passing through O will remain conserved.
$L_{i} = L_{f}$
$∴ m vL = I ω = (m L^{2} + \frac{M L ^{2}}{3}) ω$
$∴ ω = \frac{3 m v}{L ( 3 m + M )}$

Q. A rod of length L and mass M is hinged at point O. A small bullet of mass m hits the rod as shown in the figure. The bullet gets embedded in the rod. Find angular velocity of the system just after impact.

Angular momentum of the system about an axis perpendicular to plane of paper and passing through O will remain conserved. Li​=Lf​ ∴mvL=Iω=(mL2+3ML2​)ω ∴ω=L(3m+M)3mv​

Angular momentum of the system about an axis perpendicular to plane of paper and passing through O will remain conserved.
$L_{i} = L_{f}$
$∴ m vL = I ω = (m L^{2} + \frac{M L ^{2}}{3}) ω$
$∴ ω = \frac{3 m v}{L ( 3 m + M )}$