Magnetic Properties of Matter

JEE Main level, single correct, medium

34 of 57

Question 34 of 57

A thin rectangular magnet suspended freely has a period of oscillation equal to TT. Now it is broken into two equal halves (each having half of the original length) and one piece is made to oscillate freely in the same field. If its period of oscillation is T′T^{\prime}, the ratio T′T\frac{T^{\prime}}{T} is

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Answer: (B) 12\frac{1}{2}

T∝1\mathrm{T} \propto \sqrt{1}
T1T2=I1I2;I∝L2[⇒I1I2=L12 L22=(2 L2)2 L22=4]⇒T1 T2=4=2\frac{T_1}{T_2}=\sqrt{\frac{I_1}{I_2}} ; \quad \mathrm{I} \propto \mathrm{L}^2 \quad\left[\Rightarrow \frac{\mathrm{I}_1}{\mathrm{I}_2}=\frac{\mathrm{L}_1^2}{\mathrm{~L}_2^2}=\frac{\left(2 \mathrm{~L}_2\right)^2}{\mathrm{~L}_2^2}=4\right] \Rightarrow \frac{\mathrm{T}_1}{\mathrm{~T}_2}=\sqrt{4}=2
⇒T2=T12⇒T2 T1=12\Rightarrow \mathrm{T}_2=\frac{\mathrm{T}_1}{2} \Rightarrow \frac{\mathrm{T}_2}{\mathrm{~T}_1}=\frac{1}{2}

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