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  • A uniform rod of length 6m and mass 8kg lies on a smooth horizontal table as shown in the figure. Two particles having masses 2kg and 1 kg are projected to hit the rod with respective speeds of 1m/

A uniform rod of length 6m and mass 8kg lies on a smooth horizontal table as shown in the figure. Two particles having masses 2kg and 1 kg are projected to hit the rod with respective speeds of 1m/s and 2m/s. If the particle stick to the rod after the collision, find its angular velocity just after the impact. [ here a= 1m]

Option: 1

\frac{3}{5} \mathrm{rad} / \mathrm{s}


Option: 2

\frac{2}{5} \mathrm{rad} / \mathrm{s}


Option: 3

\frac{1}{5} \mathrm{rad} / \mathrm{s}


Option: 4

\frac{3}{4} \mathrm{rad} / \mathrm{s}


Answers (1)

best_answer

Conserving angular momentum about the centre of mass-

\begin{aligned} & L_{i}=2+4=6 \\ & L_{f}=\left[\frac{8 \times 6 \times 6}{12}+2 \times 1^{2}+1 \times 2^{2}\right] \omega \\ & L_{f}=[24+2+4] \omega \\ & L_{f}=30\omega \\ & 30\omega =6 \\ & \omega=\frac{1}{5} \mathrm{rad} / \mathrm{s} \end{aligned}

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SANGALDEEP SINGH

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