Question

Four $2\, kg$ masses are connected by $\frac{1}{4} m$ spokes to an axle. A force of $24\, N$ acts on a lever $1 / 2\, m$ long to produce angular acceleration $\alpha .$ The magnitude of $\alpha$ in $rad\, s ^{-2}$ is

• A. 24
• B. 12
• C. 6
• D. 3

Answer 1

Answer: (B)

As, Force $\times$ distance $=\tau=I \alpha$
$\Rightarrow F\sin 30^{\circ} \times \frac{1}{2}=4\left[2 \times\left(\frac{1}{4}\right)^{2}\right] \alpha$
or $24 \times \frac{1}{2} \times \frac{1}{2}=\frac{\alpha}{2}$
$\therefore \alpha=12\,rad\, s ^{-2}$