Question:
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 = Mv is imparted to the body at one of its end, what would be its angular velocity ?
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 = Mv is imparted to the body at one of its end, what would be its angular velocity ?
Updated On: Jun 14, 2022
- v/L
- 2v/L
- v3L
- v/4L
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The Correct Option is A
Solution and Explanation
Let $\omega$ be the angular velocity of the rod. Applying, angular impulse = change in angular momentum about centre of mass of the system
$j.\frac{L}{2}=I_c\omega$
$\therefore (Mv)\bigg(\frac{L}{2}\bigg)=(2)\bigg(\frac{ML^2}{4}\bigg)\omega$
$\therefore \omega=\frac{v}{L}$
$j.\frac{L}{2}=I_c\omega$
$\therefore (Mv)\bigg(\frac{L}{2}\bigg)=(2)\bigg(\frac{ML^2}{4}\bigg)\omega$
$\therefore \omega=\frac{v}{L}$
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Concepts Used:
System of Particles and Rotational Motion
- The system of particles refers to the extended body which is considered a rigid body most of the time for simple or easy understanding. A rigid body is a body with a perfectly definite and unchangeable shape.
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- The few common examples of rotational motion are the motion of the blade of a windmill and periodic motion.