Question

A wheel of radius $0.4m$ can rotate freely about its axis as shown in the figure. A string is wrapped over its rim and a mass of $4kg$ is hung. An angular acceleration of $8rad{s}^{-2}$ is produced in it due to the torque. Then, moment of inertia of the wheel is:

(Take $g=10{ms}^{-2}$)

• A. 2 kg-$m^2$
• B. 1 kg-$m^2$
• C. 4 kg-$m^2$
• D. 8 kg-$m^2$

Answer 1

The correct option is A 2 kg-$m^2$

Here we have to apply the torque equation from the center of the wheel.

We know that: $\tau =I\alpha$

The force due to the string is $mg=40N$ and it is given $\alpha =8rad{s}^{-2}$

$\Rightarrow 40\times 0.4=I\times 8$

$\Rightarrow I=2kg-m^2$