A circular coil has moment of inertia <math> <mn>0.8</mn> <mtext> </mtext> <mi mathvariant="normal">k</mi> <mi mathvariant="normal">g</mi> <msup> <mrow> <mrow> <mtext> </mtext> <mi mathvariant="normal">m</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msup> </math> around any diameter and is carrying current to produce a magnetic moment of <math> <mn>20</mn> <msup> <mrow> <mrow> <mi mathvariant="normal">A</mi> <mi mathvariant="normal">m</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msup> </math> . The coil is kept initially in a vertical position and it can rotate freely around a horizontal diameter. When a uniform magnetic field of <math> <mn>4</mn> <mtext> </mtext> <mi mathvariant="normal">T</mi> </math> is applied along the vertical, it starts rotating around its horizontal diameter. The angular speed the coil acquires after rotating by <math> <msup> <mrow> <mrow> <mn>60</mn> </mrow> </mrow> <mrow> <mrow> <mo>?</mo> </mrow> </mrow> </msup> </math> will be:

Sol. K=QrΔxΔAT⇒ML2T-2 (L)L2 (θ) (T)⇒M1L1-T-3θ-1

A circular coil has moment of inertia <math> <mn>0.8</mn> <mtext> </mtext> <mi mathvariant="normal">k</mi> <mi mathvariant="normal">g</mi> <msup> <mrow> <mrow> <mtext> </mtext> <mi mathvariant="normal">m</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msup> </math> around any diameter and is carrying current to produce a magnetic moment of <math> <mn>20</mn> <msup> <mrow> <mrow> <mi mathvariant="normal">A</mi> <mi mathvariant="normal">m</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msup> </math> . The coil is kept initially in a vertical position and it can rotate freely around a horizontal diameter. When a uniform magnetic field of <math> <mn>4</mn> <mtext> </mtext> <mi mathvariant="normal">T</mi> </math> is applied along the vertical, it starts rotating around its horizontal diameter. The angular speed the coil acquires after rotating by <math> <msup> <mrow> <mrow> <mn>60</mn> </mrow> </mrow> <mrow> <mrow> <mo>?</mo> </mrow> </mrow> </msup> </math> &nbsp;will be:

Ask & Answer Question

Option 1 -

$10 π r a d s^{- 1}$

Option 2 -

$20 π r a d s^{- 1}$

Option 3 -

$20 r a d s^{- 1}$

Option 4 -

$10 r a d s^{- 1}$

2 Views | Posted 3 months ago

Answered by

alok kumar singh | Contributor-Level 10

3 months ago

Correct Option - 1

Detailed Solution:

Sol. $K = \frac{(\frac{Q}{r}) Δ x}{Δ A T}$

$\begin{array}{l} \Rightarrow & \frac{({M L}^{2} T^{- 2}) (L)}{(L^{2}) (θ) (T)} \\ \Rightarrow & M^{1} L^{1 -} T^{- 3} θ^{- 1} \end{array}$

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