A hoop and a solid cylinder of same mass and radius are made of a… | JEE Main 2019 (10 Jan, Shift 2)

Q75JEE Main 2019 · 10 JAN · SHIFT 2Difficult

Current Loop as a Magnetic Dipole

A hoop and a solid cylinder of same mass and radius are made of a permanent magnetic material with their magnetic moment parallel to their respective axes. But the magnetic moment of hoop is twice of solid cylinder. They are placed in a uniform magnetic field in such a manner that their magnetic moments make a small angle with the field. If the oscillation periods of hoop and cylinder are Th and Tc respectively, then -

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Answer: (b)

For small oscillations of a dipole: $T = 2\pi\sqrt{\frac{I}{\mu B}}$ .
Hoop: $I_h = MR^2$ , $\mu_h = 2\mu$ , so $\frac{I_h}{\mu_h} = \frac{MR^2}{2\mu}$ .
Cylinder: $I_c = \frac{MR^2}{2}$ , $\mu_c = \mu$ , so $\frac{I_c}{\mu_c} = \frac{MR^2}{2\mu}$ .
The ratios are equal, so $T_h = T_c$ . The answer is (b).

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