Rotational Motion

JEE Main level, single correct, medium

145 of 280

Question 145 of 280

A cord of negligible mass is wound around the rim of a wheel supported by spokes with negligible mass. The mass of wheel is 10 kg and radius is 10 cm and it can freely rotate without any friction. Initially the wheel is at rest. If a steady pull of 20 N is applied on the cord, the angular velocity of the wheel, after the cord is unwound by 1 m , would be :

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Answer: (A) 20rad/s20 \mathrm{rad} / \mathrm{s}

WF=20×1=20 J∴ΔKE=20 J=12Iω2I=MR2=10×0.12=0.1 kg m2∴20=12×0.1×ω2⇒ω=20rad/sec\begin{aligned} & \mathrm{W}_{\mathrm{F}}=20 \times 1=20 \mathrm{~J} \\ & \therefore \quad \Delta \mathrm{KE}=20 \mathrm{~J}=\frac{1}{2} \mathrm{I} \omega^2 \\ & \mathrm{I}=\mathrm{MR}^2=10 \times 0.1^2=0.1 \mathrm{~kg} \mathrm{~m}^2 \\ & \therefore \quad 20=\frac{1}{2} \times 0.1 \times \omega^2 \\ & \Rightarrow \omega=20 \mathrm{rad} / \mathrm{sec}\end{aligned}

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