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  • Two bar magnets oscillate in a horizontal plane in earth's magnetic field with time periods of <img alt="\mathrm{3 \mathrm{~s}}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7

Two bar magnets oscillate in a horizontal plane in earth's magnetic field with time periods of \mathrm{3 \mathrm{~s}} and \mathrm{4 \! \mathrm{~s}} respectively. If their moments of inertia are in the ratio of \mathrm{3: 2,} then the ratio of their magnetic moments will be:

Option: 1

2:1


Option: 2

8:3


Option: 3

1:3


Option: 4

27:16


Answers (1)

best_answer

\mathrm{T =2 \pi \sqrt{\frac{I}{M B}} }

\mathrm{\frac{T_1}{T_2} =\frac{3}{4} \rightarrow(1) \text { (Given) } }

\mathrm{\frac{I_1}{I_2} =\frac{3}{2} \rightarrow(2) \text { (Given) } }

\mathrm{\frac{T_1}{T_2} =\sqrt{\frac{I_1}{I_2} \times \frac{M_2}{M_1}} }

\mathrm{\frac{3}{4} =\sqrt{\frac{3}{2} \times \frac{M_2}{M_1}}}

\mathrm{\frac{M_{2}}{M_{1}}=\left ( \frac{3}{4} \right )^{2}\times \frac{2}{3}}

\mathrm{\frac{M_{2}}{M_{1}}=\frac{3}{8}}

\mathrm{\therefore \frac{M_{1}}{M_{2}}=\frac{8}{3}}

Hence 2 is correct option.




 

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Riya

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