Question:
A bar magnet has a period of oscillation $T$. If a similar brass piece of the same mass is placed over it, then the number of oscillations it makes in one second is
A bar magnet has a period of oscillation $T$. If a similar brass piece of the same mass is placed over it, then the number of oscillations it makes in one second is
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Frequency $\propto \frac{1}{\sqrt{I}}$ → more inertia = slower oscillation.
Updated On: May 2, 2026
- $\frac{1}{\sqrt{2}T}$
- $\frac{\sqrt{2}}{T}$
- $\frac{1}{2T}$
- $\frac{2}{T}$
- $\frac{1}{T}$
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The Correct Option is A
Solution and Explanation
Concept:
Time period of a magnet oscillating in a magnetic field:
\[
T = 2\pi \sqrt{\frac{I}{MB}}
\]
where:
• $I$ = moment of inertia
• $M$ = magnetic moment
• $B$ = magnetic field ---
Step 1: Effect of adding brass piece
• Brass is non-magnetic → does NOT change magnetic moment $M$
• Mass increases → moment of inertia increases Since same mass is added: \[ I' = 2I \] ---
Step 2: New time period \[ T' = 2\pi \sqrt{\frac{I'}{MB}} = 2\pi \sqrt{\frac{2I}{MB}} \] \[ T' = \sqrt{2} \cdot T \] ---
Step 3: Frequency (number of oscillations per second) \[ f = \frac{1}{T'} \] \[ f = \frac{1}{\sqrt{2}T} \] ---
Step 4: Interpretation
• Adding mass → increases inertia
• System becomes harder to rotate
• Oscillation becomes slower → frequency decreases --- Final Answer: \[ \boxed{\frac{1}{\sqrt{2}T}} \]
• $I$ = moment of inertia
• $M$ = magnetic moment
• $B$ = magnetic field ---
Step 1: Effect of adding brass piece
• Brass is non-magnetic → does NOT change magnetic moment $M$
• Mass increases → moment of inertia increases Since same mass is added: \[ I' = 2I \] ---
Step 2: New time period \[ T' = 2\pi \sqrt{\frac{I'}{MB}} = 2\pi \sqrt{\frac{2I}{MB}} \] \[ T' = \sqrt{2} \cdot T \] ---
Step 3: Frequency (number of oscillations per second) \[ f = \frac{1}{T'} \] \[ f = \frac{1}{\sqrt{2}T} \] ---
Step 4: Interpretation
• Adding mass → increases inertia
• System becomes harder to rotate
• Oscillation becomes slower → frequency decreases --- Final Answer: \[ \boxed{\frac{1}{\sqrt{2}T}} \]
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