Question

The time period of a freely suspended magne is $4s$. If it is broken in length into two equal parts and one part is suspended in the same way, then the time period will be

• A. 4 s
• B. 2 s
• C. 0.5 s
• D. 0.25 s

Answer 1

Answer: (B)

Time period of a suspended magnet is given by $T=2\pi \sqrt{\frac{l}{MB}}$
Where, $I=$ moment of inertia of the magnet about the point of Suspension.
$M=$ magnetic moment
$B=$ magnetic field
When the magnet is broken in length
$T^{2^{\prime }}=2\pi \sqrt{\frac{l^{\prime }}{M^{\prime }B}}$
$\Rightarrow \frac{T}{T^{2^{\prime }}}=\sqrt{\frac{1}{I^{\prime }}\times }\sqrt{\frac{M^{\prime }}{M}}$
$=\sqrt{\frac{m{L}^2}{m^{\prime }{L}^2}}\times \sqrt{\frac{L^{\prime }}{L}}$
Here, $m$ and $m$ ' are the masses of the magnet and $L$ and $L$ 's are their lengths.
$=\sqrt{\frac{m}{m^{\prime }}}\times \sqrt{\frac{L}{L^{\prime }}}=\sqrt{\frac{m}{m/2}}\times \sqrt{\frac{L}{L/2}}=\sqrt{2}\times \sqrt{2}=2$
$\Rightarrow T^{\prime }=\frac{T}{2}=\frac{4}{2}=2s$