MHT CET · Physics · Rotational Motion
Consider a body shown in the figure, consisting of two identical balls, each of mass \(\mathrm{M}\) connected by a light right rod. If an impulse \(J=M V\) ( \(V=\) linear velocity of ball)is imparted to the body at one of its ends, what would be its angular velocity?
- A \(\frac{V}{3 L}\)
- B \(\frac{V}{4 L}\)
- C \(\frac{V}{L}\)
- D \(\frac{2 V}{L}\)
Answer & Solution
Correct Answer
(C) \(\frac{V}{L}\)
Step-by-step Solution
Detailed explanation
Impulse \(J=\Delta P\)
\(\begin{aligned} & \Rightarrow M V=2 M v^{\prime}-0 \\ & \Rightarrow v^{\prime}=\frac{V}{2}\end{aligned}\)
The rod will rotate about its COM.
Thus, \(v^{\prime}=\omega R=\omega\left(\frac{L}{2}\right)\)
\(\Rightarrow \omega=\frac{2 v^{\prime}}{L}=\frac{V}{L}\)
\(\begin{aligned} & \Rightarrow M V=2 M v^{\prime}-0 \\ & \Rightarrow v^{\prime}=\frac{V}{2}\end{aligned}\)
The rod will rotate about its COM.
Thus, \(v^{\prime}=\omega R=\omega\left(\frac{L}{2}\right)\)
\(\Rightarrow \omega=\frac{2 v^{\prime}}{L}=\frac{V}{L}\)
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