Question

A wheel of radius $0.4m$ can rotated 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 inertia of the wheel is ($g=10{ms}^{-2}$)

• A. $2kg-m^2$
• B. $1kg-m^2$
• C. $1.36kg-m^2$
• D. $8kg-m^2$

Answer 1

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

Torque acting on the wheel $\tau =mg\times R=(4\times 10)\times 0.4=16N-m$

Using $\tau =I\alpha$

where $\alpha =8rad/s^2$

Or $16=I\times 8$

$⟹I=2kg-m^2$