Question

A torque of $10N-m$ acting on a wheel at rest, rotates it through $200$ radian in $10s$, what is the moment of inertia of the wheel?

• A. $10{kg-m}^2$
• B. $15{kg-m}^2$
• C. $20{kg-m}^2$
• D. $2.5{kg-m}^2$

Answer 1

The correct option is D $2.5{kg-m}^2$

${\omega }_0=0rad/s\theta =200rad$

$\theta ={\omega }_{0}t+\frac{1}{2}\alpha t^{2}200=0+\frac{1}{2}\alpha \ast (10{)}^{2}200=50\alpha \alpha =4rad/s^2$

$\tau =I\ast \alpha 10=I\ast 4I=2.5kg-m^2$

Hence option 'D' is correct.