Two bar magnets ' P ' and ' Q ' are kept in uniform magnetic field 'B' with magnetic moments ' M_ P ' and ' M_ Q ' respectively. Magnet ' P ' is oscillating with frequency twice that of magnet ' Q '. If the moment of

Correct answer: C. M_ P =8 M_ Q The frequency of oscillation given by aligned & f_ p =(1)/(2 π) M_ p B I_P and f_ Q =(1)/(2 π) M_ Q B I_ Q & f_ p =2 f_ Q & (1)/(2 π) M_ P B I_ P =2 · (1)/(2 π) M_ Q B I_ Q & M_ P I_ P =4 M_ Q I_ Q & M_ P M_ Q =4 I_ P I_ Q =8 [ I_ P =2 I_ Q ] aligned

JEE Main

Exam: JEE Main
Subject: Physics
Chapter: Magnetic Properties of Matter

JEE Main · Physics · Magnetic Properties of Matter

Two bar magnets ' P ' and ' Q ' are kept in uniform magnetic field...

Two bar magnets '

\mathrm{P}

' and '

\mathrm{Q}

' are kept in uniform magnetic field 'B' with magnetic moments '

\mathrm{M}_{\mathrm{P}}

' and '

\mathrm{M}_{\mathrm{Q}}

' respectively. Magnet '

\mathrm{P}

' is oscillating with frequency twice that of magnet '

\mathrm{Q}

'. If the moment of inertia of the magnet '

\mathrm{P}

' is twice that of magnet '

\mathrm{Q}

' then

Options

A $\mathrm{M}_{\mathrm{Q}}=2 \mathrm{MP}_{\mathrm{P}}$
B $\mathrm{M}_{\mathrm{P}}=2 \mathrm{M}_{\mathrm{Q}}$
C $\mathrm{M}_{\mathrm{P}}=8 \mathrm{M}_{\mathrm{Q}}$
D $\mathrm{M}_{\mathrm{Q}}=8 \mathrm{M}_{\mathrm{P}}$

Correct answer

C. $\mathrm{M}_{\mathrm{P}}=8 \mathrm{M}_{\mathrm{Q}}$

Step-by-step solution

The frequency of oscillation given by

\begin{aligned} & \mathrm{f}_{\mathrm{p}}=\frac{1}{2 \pi} \sqrt{\frac{\mathrm{M}_{\mathrm{p}} \mathrm{B}}{\mathrm{I}_P}} \text { and } \mathrm{f}_{\mathrm{Q}}=\frac{1}{2 \pi} \sqrt{\frac{\mathrm{M}_{\mathrm{Q}} \mathrm{B}}{\mathrm{I}_{\mathrm{Q}}}} \\ & \mathrm{f}_{\mathrm{p}}=2 \mathrm{f}_{\mathrm{Q}} \\ & \frac{1}{2 \pi} \sqrt{\frac{\mathrm{M}_{\mathrm{P}} \mathrm{B}}{\mathrm{I}_{\mathrm{P}}}}=2 \cdot \frac{1}{2 \pi} \sqrt{\frac{\mathrm{M}_{\mathrm{Q}} \mathrm{B}}{\mathrm{I}_{\mathrm{Q}}}} \\ & \frac{\mathrm{M}_{\mathrm{P}}}{\mathrm{I}_{\mathrm{P}}}=4 \frac{\mathrm{M}_{\mathrm{Q}}}{\mathrm{I}_{\mathrm{Q}}} \\ & \therefore \frac{\mathrm{M}_{\mathrm{P}}}{\mathrm{M}_{\mathrm{Q}}}=4 \frac{\mathrm{I}_{\mathrm{P}}}{\mathrm{I}_{\mathrm{Q}}}=8 \quad\left[\because \mathrm{I}_{\mathrm{P}}=2 \mathrm{I}_{\mathrm{Q}}\right] \end{aligned}

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