JEE PYQ: Oscillations Question 34
Question 34 - 2019 (10 Jan 2019 Shift 2)
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 $T_h$ and $T_c$ respectively, then:
(1) $T_h = T_c$
(2) $T_h = 2T_c$
(3) $T_h = 1.5T_c$
(4) $T_h = 0.5T_c$
Show Answer
Answer: (1)
Solution
$T = 2\pi\sqrt{\frac{I}{MB}}$. $\frac{I_h}{M_h} = \frac{mR^2}{2M_c}$ and $\frac{I_c}{M_c} = \frac{mR^2/2}{M_c}$. Both ratios are equal, so $T_h = T_c$.
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