Rotation 2 Question 18
18. A horizontal circular platform of radius $0.5 m$ and mass $0.45 kg$ is free to rotate about its axis. Two massless spring toy-guns, each carrying a steel ball of mass
$0.05 kg$ are attached to the platform at a distance $0.25 m$ from the centre on its either sides along its diameter (see figure). Each gun simultaneously fires the balls horizontally and perpendicular to the diameter in opposite directions. After leaving the platform, the balls have horizontal speed of $9 ms^{-1}$ with respect to the ground. The rotational speed of the platform in rad $s^{-1}$ after the balls leave the platform is
(2014 Adv.)
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Answer:
Correct Answer: 18. 4
Solution:
- Applying conservation of angular momentum
$$ \begin{aligned} 2 m v r-\frac{M R^{2}}{2} \omega & =0 \\ \omega & =\frac{4 m v r}{M R^{2}} \end{aligned} $$
Substituting the values, we get
$$ \omega=\frac{(4)\left(5 \times 10^{-2}\right)(9) \frac{1}{4}}{45 \times 10^{-2} \times \frac{1}{4}} \Rightarrow \omega=4 rad / s $$
