Rotational Motion

JEE Main level, single correct, medium

175 of 280

Question 175 of 280

A metal coin of mass 5g5g and radius 1cm1cm is fixed to a thin stick ABAB of negligible mass as shown in the figure. The system is initially at rest. The constant torque, that will make the system rotate about ABAB at 2525 rotations per second in 5s5s , is close to:

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Answer: (B) 2.0×10−5Nm2.0\times {10}^{-5}Nm

As torque τ\tau is constant.
ω=τIt\omega =\dfrac{\tau }{I}t
τ=ωIt=(2πn)×54mr2t\tau =\dfrac{\omega I}{t}=\dfrac{\left(2\pi n\right)\times \dfrac{5}{4}m{r}^{2}}{t}
=(2π×25)×54×5×10−3×(1×10−2)25=\dfrac{\left(2\pi \times 25\right)\times \dfrac{5}{4}\times 5\times {10}^{-3}\times {\left(1\times {10}^{-2}\right)}^{2}}{5}
=196×10−7=196\times {10}^{-7}
≈2⋅0×10−5Nm\approx 2\cdot 0\times {10}^{-5} Nm

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