Question

A hoop and a solid cylinder of same mass and radius are made of a permanent magnetic material with 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:

• A. $T_h=2T_c$
• B. $T_h=T_c$
• C. $T_h=0.5T_c$
• D. $T_h=1.5T_c$

Answer 1

Answer: (B)

Time period of any magnetic body place in an external magnetic field is:-
$T=2\pi \sqrt{\frac{I}{MB}}$
$T_{hoop}=2\pi \sqrt{\frac{m{R}^2}{MB}}$ ...... $(1)$ $I_{hoop}=m{R}^2$
$T_c=2\pi \sqrt{\frac{\frac{m{R}^2}{2}}{\frac{M}{2}\left(B\right)}}$ ...... $(2)$ $I_{\text{Solid cylinder}}=\frac{m{R}^2}{2}$
From $(1)$ and $(2)$
$T_h=T_c$