Question

A metal coin of mass $5\,g$ and radius $1\, cm$ is fixed to a thin stick $AB$ of negligible mass as shown in the figure. The system is initially at rest. The constant torque, that will make the system rotate about $AB$ at $25$ rotations per second in $5\, s$, is close to :

• A. $4.0 \times 10^{-6} $ Nm
• B. $2.0 \times 10^{-5} $ Nm
• C. $1.6 \times 10^{-5} $ Nm
• D. $7.9 \times 10^{-6} $ Nm

Answer 1

The Correct Option is B

$\alpha =\frac{\Delta\omega}{\Delta t} = \frac{25\times2\pi}{5} =10\pi \text{rad}/\sec^{2} $
$ \tau = \left(\frac{5}{4} MR^{2}\right)\alpha $
$= \frac{5}{4} \times5\times 10^{-3} \times \left(10^{-2}\right)^{2} \times 10\pi $
$ = 1.9625 \times 10^{-5} Nm $
$ \simeq 2.0 \times 10^{-5} Nm $