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Question
Equal torques act on the disc A and B of the previous problem, initially both being at rest. At a later instant, the linear speeds of a point on the rim of A and another point on the rim of B are \[\nu_A\] and \[\nu_B\] respectively. We have
Options
\[\nu_A>\nu_B\]
\[\nu_A=\nu_B\]
\[\nu_A<\nu_B\]
the relation depends on the actual magnitude of the torques
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Solution
\[\nu_A>\nu_B\]
\[\tau = I\alpha \left(\text{magnitude} \right)\]
For equal torque, we have
\[I_A \alpha_A = I_B \alpha_B\]
IA < IB
⇒ \[\alpha_A > \alpha_B ...........(1)\]
Now,
\[\omega = \alpha t\]
Or,
\[\frac{v}{r} = \alpha t\]
\[\nu_A > \nu_B.............\left(\text{Using (1)}\right)\]
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