A bar magnet is oscillating in the Earth's magnetic field with a period T. What happens to its period and motion if its mass is quadrupled? (a) motion remains simple harmonic with time period = T/2 (b) motion remains S.H.M with time period = 2T (c) motion remains S.H.M with time period = 4T (d) motion remains S.H.M and period remains nearly constant

Answer: (b). T = 2π√(I/MBH) and I ∝ m (same shape), so T ∝ √(m). The restoring torque is still ∝ θ for small angles, so the motion stays SHM. m' = 4m ⇒ T' = √(4) T = 2T So the answer is (b) SHM with period 2T.

A bar magnet is oscillating in the Earth's magnetic field with a… | NEET 2003 (AIPMT)

Q17NEET 2003 · AIPMTMedium

Vibration Magnetometer

A bar magnet is oscillating in the Earth's magnetic field with a period T. What happens to its period and motion if its mass is quadrupled?

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Answer: (b)

$T = 2\pi\sqrt{\dfrac{I}{MB_H}}$ and $I \propto m$ (same shape), so $T \propto \sqrt{m}$ .
The restoring torque is still $\propto \theta$ for small angles, so the motion stays SHM.
$m' = 4m \Rightarrow T' = \sqrt{4}\,T = 2T$
So the answer is (b) SHM with period $2T$ .

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