A wheel of radius 0.4 m can rotate freely about its axis as shown...

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 \mathrm{~rad/s}^{-2}

is produced in it due to the torque. Then, moment of inertia of the wheel is

\left(g=10 \mathrm{~ms}^{-2}\right)

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

Options

A $2 \mathrm{~kg}-\mathrm{m}^2$
B $1 \mathrm{~kg}-\mathrm{m}^2$
C $4 \mathrm{~kg}-\mathrm{m}^2$
D $8 \mathrm{~kg}-\mathrm{m}^2$

Correct answer

A. $2 \mathrm{~kg}-\mathrm{m}^2$

Step-by-step solution

Given,

\quad r=0.4 \mathrm{~m}

\alpha=8 \mathrm{~rad}/ \mathrm{s}^{-1}

m=4 \mathrm{~kg}, \quad I=

? Torque,

\quad \tau=I \alpha

m g r=I \cdot \alpha

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

\Rightarrow \quad I=\frac{16}{8}=2 \mathrm{~kg}-\mathrm{m}^2

I=2 \mathrm{~kg}-\mathrm{m}^2

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