Question

A uniform disc of mass $M$ and radius $R$ is hinged at its centre $C$. A force $F$ is applied on the disc as shown. At this instant, angular acceleration of the disc is:

• A. $\sqrt{3}\frac{F}{MR}$
• B. $\frac{F}{MR}$
• C. $\frac{2}{\sqrt{3}}\frac{F}{MR}$
• D. $\frac{F}{2MR}$

Answer 1

Answer: (B)

$\frac{F}{MR}$

Given,
mass of uniform disc $=M$
radius of uniform disc $=R$
applied force on disc $=F$
According to the question, we can draw the diagram as following
We know that, $\tau =I\alpha$
$\Rightarrow F\sin {30}^{\circ }R=\frac{M{R}^2}{2}\alpha$
$\Rightarrow F\times \frac{1}{2}\times R=\frac{M{R}^2}{2}\alpha$
$\Rightarrow \alpha =\frac{F}{MR}$.