Question

In figure (a), a metre stick, half of which is wood and the other half steel is pivoted at the wooden end at $O$ and a force is applied to the steel end at $a$. In figure (b), the stick is pivoted at the steel end at $O^{\prime }$ and the same force is applied at the wooden end at $a^{\prime }$. The angular acceleration

• A. in (a) is greater than in (b)
• B. in (b) is greater than in (a)
• C. equal in both (a) and (b)
• D. none of the above

Answer 1

The correct option is B in (b) is greater than in (a)

Steel is denser than wood.
We know that $\tau =I\times \alpha$
Here, $I=$ moment of inertia
$\tau =$ torque,
$\alpha =$ angular acceleration,
$\Rightarrow \tau =I\alpha =$ constant
$\Rightarrow \alpha =\frac{\tau }{I}$
$\Rightarrow \alpha \propto \frac{1}{I}$
Here, $\tau$ is the same in both cases, but $I_1>I_2$,
hence ${\alpha }_1<{\alpha }_2$
Angular acceleration will be more, when $I$ is small, for which lighter material (wood) should at longer distance from the axis of rotation i.e. when stick is pivoted at the steel end.