Rankers Physics

Magnetic Properties of Matter: Practice Problem & Solution

16. 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? (2003)
Motion remains S.H.M. with time $text{period} = frac{T}{2}$
Motion remains S.H.M. with time $text{period} = 2T$
Motion remains S.H.M. with time $text{period} = 4T$
Motion remains S.H.M and period remains nearly constant

Solution Explained:

To solve this problem, we apply the core principles of Magnetic Properties of Matter. Understanding the underlying formula is key to arriving at the correct answer below:

The period of oscillation is $T = 2pisqrt{frac{I}{MB}}$. Moment of inertia $I propto m$. If mass is quadrupled, $I' = 4I$, so $T' = 2pisqrt{frac{4I}{MB}} = 2T$. The motion continues to be simple harmonic.

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