Question:
A thin circular ring of mass $ M $ and radius $ r $ is rotating about its axis with constant angular velocity $ \omega $ . Two objects each of mass $ m $ , are placed gently at the opposite ends of diameter of the ring. The ring now rotates with an angular velocity
A thin circular ring of mass $ M $ and radius $ r $ is rotating about its axis with constant angular velocity $ \omega $ . Two objects each of mass $ m $ , are placed gently at the opposite ends of diameter of the ring. The ring now rotates with an angular velocity
Updated On: Jul 2, 2022
- $ \omega M/(M+m) $
- $ \omega M/(M+2m) $
- $ \omega (M-2m)/(m+2M) $
- $ \omega (M+2m)/M $
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The Correct Option is B
Solution and Explanation
As on torque is acting on the system, so from law of conservation of angular momentum, Initial angular momentum
= final angular momentum .
i.e., $M r^{2} \omega=(M+2 m) r^{2} \omega$
$\Rightarrow \omega'=\frac{M \omega}{(M+2 m)}$
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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.
- The distance between the pair of particles in such a body does not replace or alter. Rotational motion can be described as the motion of a rigid body originates in such a manner that all of its particles move in a circle about an axis with a common angular velocity.
- The few common examples of rotational motion are the motion of the blade of a windmill and periodic motion.