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Q.

A conducting ring of mass 2 kg and radius 0.5 m is placed on the smooth horizontal plane. The ring carries a current i = 4A. A horizontal magnetic field B = 10t is switched on at t = 0 as shown in figure. The ring is left free to move at t = 1 second. The angular acceleration of the ring is at t = 1 second is

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a

$5 π r a d / s^{2}$

b

$15 π r a d / s^{2}$

c

$20 π r a d / s^{2}$

d

$40 π r a d / s^{2}$

answer is D.

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Detailed Solution

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$M = i A (- \overset{\land}{K}) = - 4 π {(0.5)}^{2} \overset{\land}{K} \begin{array}{l} \vec{M} = - π \overset{\land}{K} \\ T = \vec{M} \times \vec{B} = - (π \overset{\land}{K}) \times 10 \overset{\land}{i} = - 10 π \overset{\land}{J} \\ l = \frac{m R^{2}}{2} = \frac{1}{2} 2 {(0.5)}^{2} = \frac{1}{4} \\ α = \frac{T}{I} = \frac{10 π}{\frac{1}{4}} = 40 π r a d / s^{2} \end{array}$

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A conducting ring of mass 2 kg and radius 0.5 m is placed on the smooth horizontal plane. The ring carries a current i = 4A. A horizontal magnetic field B = 10t is switched on at t = 0 as shown in figure. The ring is left free to move at t = 1 second. The angular acceleration of the ring is at t = 1 second is