Question

A triangular plate of uniform thickness and density is made to rotate about an axis perpendicular to the plane of the paper and (a) passing through $A$, (b) passing through $B$, by the application of some force $F$ at $C$ (mid-point of $AB$) as shown in the figure. In which case, the angular acceleration is more?

• A. In case (a)
• B. In case (b)
• C. Same in both cases
• D. Cannot be determined

Answer 1

The correct option is B In case (b)

Using Newton's law for rotational motion,
$\tau =I\alpha$ or $\alpha =\frac{\tau }{I}$
Here, as the force is applied at the mid-point,
${\tau }_A={\tau }_B=F\times \frac{L}{2}$

As moment of inertia depends on the distribution of mass with respect to the axis of rotation, $I_A>I_B$

Hence, ${\alpha }_A<{\alpha }_B$
i.e. angular acceleration is more in case (b).
Hence, the correct answer is option (b).