Question

Time period for a thin magnet is $T$ . If it is divided into four equal parts, then time period for each part will be :

• A. $4T$
• B. $T/4$
• C. $T/2$
• D. $T$

Answer 1

Answer: (C)

$T/2$

Let the length of the magnet is $l$.

The new mass and length is given as,

$m^{\prime }=\frac{m}{2}$

$l^{\prime }=\frac{l}{2}$

$M^{\prime }=\frac{m}{2}\times \frac{l}{2}$

$M^{\prime }=\frac{M}{4}$

The new moment of inertia is given as,

$I^{\prime }=\frac{M^{\prime }{l^{\prime }}^2}{12}$

$I^{\prime }=\frac{\left(\frac{M}{4}\right){\left(\frac{l}{2}\right)}^2}{12}$

$I^{\prime }=\frac{1}{16}\frac{\left(M\right){\left(l\right)}^2}{12}$

$I^{\prime }=\frac{I}{16}$

The time period of each part is given as,

$T^{\prime }=2\pi \sqrt{\frac{I/16}{\left(M/4\right)B_H}}$

$T^{\prime }=\frac{T}{2}$

Thus, the time period of each part is $\frac{T}{2}$.