Q.
A wheel of radius $0.4\ m$ can rotate freely about its axis as shown in the figure. A string is wrapped over its rim and a mass of $4\ kg$ is hung. An angular acceleration of $8\ rad$-$s^{- 2}$ is produced in it due to the torque. Then, moment of inertia of the wheel is $(g = 10\ ms^{- 2})$
A) $2kg - m^{2}$
B) $1\ kg - m^{2}$
C) $4\ kg - m^{2}$
D) $8\ kg - m^{2}$
Explanation
(a) Given, $r = 0.4m,\ \alpha = 8\ rad\ s^{- 2}$
$m = 4kg,\ I = ?$
Torque, $\tau = I\alpha = mgr \Rightarrow 4 \times 10 \times 0.4 = I \times 8$
$\Rightarrow I = \frac{16}{8} = 2kg - m^{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.