Rotation 4 Question 1
2. Consider a body, shown in figure, consisting of two identical balls, each of mass $M$ connected by a light rigid rod. If an impulse $J=M v$ is imparted to the body at one of its end, what would be its angular velocity?
(2003)
(a) $v / L$
(b) $2 v / L$
(c) $v / 3 L$
(d) $v / 4 L$
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Answer:
Correct Answer: 2. (a)
Solution:
- Let $\omega$ be the angular velocity of the rod. Applying, angular impulse $=$ change in angular momentum about centre of mass of the system
$$ \begin{array}{rlrl} & \text { (M) } \\ \therefore \quad & (M v) \frac{L}{2} & =I _c \omega \\ & & =(2) \frac{M L^{2}}{4} \omega \\ & \omega & =\frac{v}{L} \end{array} $$
