A magnet is cut in four equal parts by cutting it parallel to its...

A magnet is cut in four equal parts by cutting it parallel to its length. The time period of each part, if the time period of the original magnet in the same field is ${T}_{0}$ , will be

Options

A ${T}_{0}$
B $\dfrac{T0}{2}$
C $\dfrac{T0}{4}$
D $4{T}_{0}$

Correct answer

A. ${T}_{0}$

Step-by-step solution

For each part,

{I}_{1} = \dfrac{I}{4} and

{M}_{1} = \dfrac{M}{4}

.<br /><br />

∴ T = 2\pi\sqrt{

\left(\dfrac{I}{MB}\right)}

and

{T}_{1} = 2\pi\sqrt{\left(\dfrac{I1}{{M}_{1}B}\right)}

= 2\pi\sqrt{\left(\dfrac{I \times 4}{4M \times B}\right)}

∴ \dfrac{T1}{T} = 1

∴ {T}_{1} = T = {T}_{0}

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