Question

Two bar magnets of the same mass, same length and breadth but having magnetic moments $M$ and $3M$ are joined together pole for pole and suspended by a string.
The time period of assembly in a magnetic field of strength $1$ $H$ is $3$ $s$ . If now the polarity of one of the magnets is reversed and the combination is again made to oscillate in the same field, the time of oscillation is

• A. $3 \, \text{s}$
• B. $3\sqrt{3}$ $s$
• C. $3/\sqrt{3}\text{ s}$
• D. $3\sqrt{2}\text{s}$

Answer 1

Answer: (D)

In pole for pole combination,
$M_{1}=3M+M= 4M$
and if the polarity is reversed $\textit{M}_{2}=3\textit{M}-\textit{M}=2\textit{M}$
$\textit{T}_{2}=?$
$\frac{\textit{T}_{2}}{\textit{T}_{1}}=\sqrt{\frac{M_{1}}{M_{2}}}=\sqrt{\frac{4 \, M}{2 M}}$
$\textit{T}_{2}=\sqrt{2}\textit{T}_{1}=3\sqrt{2}\text{s}$