A) \[\left( \frac{M-2m}{M+m} \right)\omega \]
B) \[\left( \frac{M+2m}{M+m} \right)\omega \]
C) \[\left( \frac{M-2m}{M-m} \right)\omega \]
D) \[\left( \frac{M+2m}{M-m} \right)\omega \]
Correct Answer: C
Solution :
Key Idea: Angular momentum remains conserved. From law of conservation of angular momentum if no external torque is acting upon a body rotating about an axis, then the angular momentum of the body remains constant. \[J=I\omega =\text{constant}\] (\[\omega =\] angular velocity) Moment of inertia of disc \[=\frac{1}{2}M{{R}^{2}}\] \[\therefore \] \[\frac{1}{2}M{{R}^{2}}\omega =\frac{1}{2}(M-m){{R}^{2}}\omega +m{{R}^{2}}\omega \] \[\Rightarrow \] \[(M-m)\omega =M\omega -2m\omega \] \[\Rightarrow \] \[\omega =\frac{(M-2m)}{(M-m)}\omega \]You need to login to perform this action.
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