SATHEE: Rotation 2 Question 22

Rotation 2 Question 22

22. A smooth uniform rod of length $L$ and mass $M$ has two identical beads of negligible size, each of mass $m$ , which can slide freely along the rod. Initially, the two beads are at the centre of the rod and the system is rotating with an angular velocity $ω_{0}$ about an axis perpendicular to the rod and passing through the mid-point of the rod (see figure).

There are no external forces. When the beads reach the ends of the rod, the angular velocity of the system is…… .

$(1988, 2 M)$

True/False

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Answer:

Correct Answer: 22. $\frac{M ω_{0}}{M + 6 m}$

Solution:

$I_{1} ω_{1} = I_{2} ω_{2}$

$\begin{aligned} ∴ ω_{2} & = \frac{I_{1}}{I_{2}} \cdot ω_{1} = \frac{(M L^{2} / 12)}{[(M L^{2} / 12) + 2 m (L / 2)^{2}]} ω_{0} \\ = \frac{M L^{2}}{M L^{2} + 6 m L^{2}} ω_{0} = \frac{M}{M + 6 m} ω_{0} \end{aligned}$

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Rotation 2 Question 22

True/False

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