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  • A conducting ring of mass and radius <img alt="0.5 \mathrm{~m}" src="https://entrancecorne

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

 

Option: 1

40 \pi \ \mathrm{rad} / \mathrm{s}^2


Option: 2

20 \pi \ \mathrm{rad} / \mathrm{s}^2


Option: 3

5 \pi \ \mathrm{rad} / \mathrm{s}^2


Option: 4

15 \pi \ \mathrm{rad} / \mathrm{s}^2


Answers (1)

\begin{aligned} \quad \vec{\tau} & =I \alpha \\ \Rightarrow \quad B i r\left(R^2\right) & =\frac{m R^2}{2} \alpha \\ \Rightarrow \quad \alpha & =\frac{2 B i \pi}{m} \\ & =\frac{2 \times 10 \times 4 \pi}{2} \\ & =\operatorname{40} \mathrm{rad} / \mathrm{s}^2 \end{aligned}

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Kshitij

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