In a uniform magnetic field of 0.049 T, a magnetic needle performs 20 complete oscillations in 5 seconds as shown. The moment of inertia of the needle is 9.8*106 kg m2 . If the magnitude of magnetic moment of the needle is x*105Am2 , then the value of ' x  ' is :

 

Option 1 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mn>5</mn> <msup> <mrow> <mi>π</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> </math> </span></p>
Option 2 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mn>1</mn> <mn>2</mn> <mn>8</mn> <msup> <mrow> <mi>π</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> </math> </span></p>
Option 3 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mn>5</mn> <mn>0</mn> <msup> <mrow> <mi>π</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> </math> </span></p>
Option 4 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mn>1</mn> <mn>2</mn> <mn>8</mn> <mn>0</mn> <msup> <mrow> <mi>π</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> </math> </span></p>
10 Views|Posted 7 months ago
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1 Answer
A
7 months ago
Correct Option - 4
Detailed Solution:

Time period of Oscillation, T = 2 π I M B

1 4 = 2 π 9 . 8 * 1 0 6 M * 0 . 0 4 9

1 1 6 = 4 π 2 * 9 . 8 * 1 0 6 M * 4 9 * 1 0 3

M = 4 π 2 * 9 . 8 * 1 0 6 4 9 * 1 0 3 * 1 6

= 4 π 2 * 9 . 8 * 1 6 * 1 0 3 4 9

= 1 2 . 8 π 2 * 1 0 3 * 1 0 2 * 1 0 2

=1280π2*105Am2

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Physics Magnetism and Matter 2025

Physics Magnetism and Matter 2025

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