Question

The time period of a freely suspended magnet is 4s. If it is broken in length into two equal

Answer 1

If magnet is broken into two equal parts

so te time period will remains the same because time period does not depends upon the mass of suspended sustance

hope it is helpfull

Answer 2

Answer:

The new time period is 2 sec.

Explanation:

Given that,

Time = 4 sec

Suppose If it is broken in length into two equal and one part is suspended in the same way, then its time period will be

We need to calculate the time period

Using formula of time period

$T=2\pi\sqrt{\dfrac{I}{M_{B}}}$

Moment of inertia of rod is

$I=\dfrac{Ml^2}{12}$

Moment of inertia for half length,

$I'=\dfrac{\dfrac{m}{2}\times\dfrac{l^2}{4}}{12}$

$I'=\dfrac{ml^2}{12}\times\dfrac{1}{8}$

$I'=\dfrac{I}{8}$

Magnetic moment is

$M'=\dfrac{M}{2}$

We need to calculate the new time period

$T'=2\pi\sqrt{\dfrac{I'}{M'_{B}}}$

Put the value into the formula

$T'=2\pi\sqrt{\dfrac{\dfrac{I}{8}}{\dfrac{M_{B}}{2}}}$

$T'=\dfrac{1}{2}\times2\pi\sqrt{\dfrac{I}{M_{B}}}$

$T'=\dfrac{T}{2}$

Put the value of T into the formula

$T'=\dfrac{4}{2}$

$T'=2\ sec$

Hence, The new time period is 2 sec.