Question

On quadrupling the moment of inertia of a magnet, its frequency of oscillation will become: *

4 points

(a) half

(b) double

(c) four times

(d) one-fourth​

Answer 1

The moment of inertia of a magnet:

Explanation:

The time period of the moment is given by

$\displaystyle T = 2\pi \sqrt{\frac{I}{MB} }$

But frequency is the inverse of a time period

∴  $\displaystyle f = \frac{1}{2\pi } \sqrt{\frac{MB}{I} }$

where

f = frequency of the oscillation

M = magnetic dipole moment

B =  magnetic field

I = moment of inertia of a magnet

This shows that

f ∝ $\sqrt{\frac{1}{I} }$

When the moment of inertia is quadrupled

i.e. f ∝ $\sqrt{\frac{1}{4} }$

f  ∝ $\mathbf {\frac{1}{2}}$

Option 4 is correct.

Answer 2

Answer:

Option (a) is correct.

Hope this will help you

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