Question

A conducting ring of mass $2kg$ and radius $0.5m$ is placed on a smooth horizontal plane. The ring carries a current of $i=4A$.
A horizontal magnetic field $B=10T$ is switched on at time $t=0$ as shown in figure. The initial angular acceleration of the ring will be:

• A. $40\pi rad{s}^{-2}$
• B. $20\pi rad{s}^{-2}$
• C. $5\pi rad{s}^{-2}$
• D. $15\pi rad{s}^{-2}$

Answer 1

The correct option is A $40\pi rad{s}^{-2}$

Due to torque of magnetic field, ring will rotate about axis passing through centre which is perpendicular to plane of paper.
$\tau =I\alpha$
$MB=I\alpha$
$i\pi r^{2}B=\frac{1}{2}m{r}^2\alpha$
$\alpha =\frac{2iB\pi }{m}=\frac{2\times 4\times 10\pi }{2}=40\pi rad{s}^{-2}$