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 `4 kg` is hung. An angular acceleration of `8 rad//s^(2)` is produced in it due to the torque. Then, the moment of inertia of the wheel is (`g=10m//s^(2)`)

Options

A. 2kg `-m^(2)`
B. `1 kg -m^(2)`
C. `4 kg -m^(2)`
D. `8 kg -m^(2)`

Answer

A

Explanation

Given, r=04 m , `alpha=8 rad s^(-2)`
`m=4 kg , I=?`
Torque , `tau=I alpha = mgr rArr 4xx10xx0.4=1xx8 rArr I=16/8= 2 kg -m^(2)`