Question

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. angular acceleration of 8 rad-$s^{-2}$ is produced in it due to the torque. the moment of inertia of wheel is $(g=10m{s}^{-2}O)$

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

Answer 1

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

We know that Torque $=r\times f$

Given, $R=0.4m$

$\alpha =8rad/s^2$

$M=4kg$

So,

by equation of torque,

$I\times \alpha =R\times F$

$I\times 8=0.4\times mg$

$I\times 8=0.4\times 10\times 4$

or, $I=\frac{4}{10}\times 10\times 8\times 4$

$=2kg-m^2$