Question

A magnet is cut in three equal parts by cutting it perpendicular to its length. The time period of original magnet is T${}_0$ in a uniform magnetic field B. Then, the time period of each part in the same magnetic field is

• A. $\frac{T_0}{2}$
• B. $\frac{T_0}{3}$
• C. $\frac{T_0}{4}$
• D. None of these

Answer 1

Answer: (B)

$\frac{T_0}{3}$

Initially the time period of magnet=$T_0=2\pi \sqrt{\frac{I}{MB}}$

where $I$ is the moment of inertia of the bar magnet

$M$ is the magnetic moment of the bar magnet

When the magnet is cut in three equal parts, the magnetic moment of each bar becomes $\frac{M}{3}=M^{\prime }$.

Also the new moment of inertia becomes $I^{\prime }=\frac{I}{3^3}=\frac{I}{27}$

Hence, the new time period becomes $T^{\prime }=2\pi \sqrt{\frac{I^{\prime }}{M^{\prime }B}}$ $=\frac{T_0}{3}$