Question

A long magnet is cut into two equal parts, such that the length of each half is same as that of original magnet. If the period of original magnet is $T$, the period of new magnet is

• A. $T$
• B. $\frac{T}{2}$
• C. $\frac{T}{4}$
• D. $2T$

Answer 1

Answer: (A)

$T$

Answer 2

Time period $T=2 \pi \sqrt{\frac{I}{M B}}$
As the magnet is cut into two equal parts along axis, then for each part
$I'=\frac{I}{2}$
$M'=\frac{M}{2}$
$\therefore$ Time period of new magnet,
$T'=\sqrt{\frac{I'}{M' B'}}$
$=\sqrt{\frac{I \times 2}{2 \times M \times B}}$
$T'=T$