Question:
A thin circular ring of mass m and radius R is rotating about its axis with a constant angular velocity $\omega.$Two objects each of mass M are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with an angular velocity $\omega.$' = :
A thin circular ring of mass m and radius R is rotating about its axis with a constant angular velocity $\omega.$Two objects each of mass M are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with an angular velocity $\omega.$' = :
Updated On: Aug 15, 2022
- $\frac{\omega\left(m+2M\right)}{m}$
- $\frac{\omega\left(m-2m\right)}{\left(m+2M\right)}$
- $\frac{\omega m}{\left(m+M\right)}$
- $\frac{\omega m}{\left(m+2M\right)}$
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The Correct Option is D
Solution and Explanation
As no external torque is acting about the axis, angular momentum of system remains conserved.
$I_{1} \omega=I_{2} \omega'$
$\Rightarrow\,\quad mR^{2}\omega=\left(mR^{2}+2MR^{2}\right)\omega'$
$\Rightarrow\,\quad\omega'=\left(\frac{m}{m+2M}\right)\omega$
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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.