A wheel of radius 0.2 m rotates freely about its center when a...

A wheel of radius 0.2 m rotates freely about its center when a string that is wrapped over its rim is pulled by force of 10 N as shown in figure. The established torque produces an angular acceleration of

2 \mathrm{~rad} / \mathrm{s}^2

. Moment of inertia of the wheel is _____

\mathrm{kg} \mathrm{m}^2

.
(Acceleration due to gravity

=10 \mathrm{~m} / \mathrm{s}^2

)

Correct answer

Step-by-step solution

\begin{aligned} & \mathrm{FR}=\mathrm{I} \alpha \\ & \Rightarrow \mathrm{I}=\frac{\mathrm{FR}}{\alpha}=\frac{10 \times 0.2}{2}=1 \mathrm{~kg}-\mathrm{m}^2\end{aligned}

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