Question

Time period of a bar magnet oscillating in earth's magnetic field is T. Its magnetic moment is M. Now, a bar magnet of magnetic moment $2$M is brought near it. The new time period will. be

• A. $T$
• B. $\frac{T}{\sqrt{3}}$
• C. $T\sqrt{3}$
• D. $3T$

Answer 1

Answer: (B)

$\frac{T}{\sqrt{3}}$

we know,

Time Period of a magnet in a magnetic field is $=2\pi \sqrt{\frac{I}{M.B}}$

now,$M_i=M$ and $M_f=3m$

$T_i=2\pi \sqrt{\frac{I}{M.B}}$

$T_f=2\pi \sqrt{\frac{I}{3.M.B}}$ $=\frac{1}{\sqrt{3}}\times 2\pi \sqrt{\frac{I}{M.B}}$

$T_f=\frac{1}{\sqrt{3}}{T}_i$

Hence, Option $\text{B}$ is correct.