KVPY Sample Paper KVPY Stream-SX Model Paper-28

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:

A) \[{{T}_{h}}={{T}_{c}}\]

B) \[{{T}_{h}}=2{{T}_{c}}\]

C) \[{{T}_{h}}=1.5{{T}_{c}}\]

D) \[{{T}_{h}}={{0.5}_{c}}\]

Correct Answer: A

Solution :

\[\because \] \[T=2\pi \sqrt{\frac{1}{\mu B}}\]

\[\frac{{{T}_{h}}}{{{T}_{c}}}=\sqrt{\frac{{{I}_{R}}}{{{I}_{c}}}\times \frac{{{\mu }_{c}}}{{{\mu }_{h}}}}\]

\[=\sqrt{2\times \frac{1}{2}}=1\]

\[{{T}_{h}}={{T}_{c}}\]