A vibration magnetometer consists of two identical bar magnets...

A vibration magnetometer consists of two identical bar magnets placed one over the other such that they are mutually perpendicular and bisect each other. The time period of the combination is

4s

. If one of the magnets is removed, then the time period of other one will be

Options

A $\text{5.78}s$
B $\text{3.36}s$
C $\text{4.36}s$
D $\text{5.36}s$

Correct answer

B. $\text{3.36}s$

Step-by-step solution

As magnets are perpendicular to each other, the resultant magnetic moment

M ' = \sqrt{M^{2} + M^{2}} = \sqrt{2}M

∴ {T}_{1} = 2\pi\sqrt{\dfrac{2I}{\left(\sqrt{2}M\right)H}}

<br /><br />In the second case,

{T}_{2} = 2\pi\sqrt{\dfrac{I}{MH}}

<br /><br />

\dfrac{T2}{T1} = \dfrac{1}{\left(2\right)1 / 4}

<br /><br />

∴ {T}_{2} = \dfrac{4}{\left(2\right)1 / 4} = \text{3.36}s

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