A magnet is cut in four equal parts by cutting it parallel to its length. The time period of each part, if the time period of the original magnet in the same field is T0 , will be

Question

A magnet is cut in four equal parts by cutting it parallel to its length. The time period of each part, if the time period of the original magnet in the same field is T0 , will be (A) T0 (B) (T0/2) (C) (T0/4) (D) 4T0

Tardigrade Admin · Accepted Answer

For each part, I1=(I/4) and M1=(M/4) . ∴ T=2π √((I/MB)) and T1=2π √((I1/M1 B)) =2π √((I × 4/4 M × B)) ∴ (T1/T)=1 ∴ T1=T=T0

Q. A magnet is cut in four equal parts by cutting it parallel to its length. The time period of each part, if the time period of the original magnet in the same field is $T_{0}$ , will be

$T_{0}$

$\frac{T _{0}}{2}$

$\frac{T _{0}}{4}$

$4 T_{0}$

For each part, $I_{1} = \frac{I}{4}$ and $M_{1} = \frac{M}{4}$ .
$∴ T = 2 π (\frac{I}{MB})$ and $T_{1} = 2 π (\frac{I _{1}}{M _{1} B})$
$= 2 π (\frac{I \times 4}{4 M \times B})$
$∴ \frac{T _{1}}{T} = 1$
$∴ T_{1} = T = T_{0}$

Q. A magnet is cut in four equal parts by cutting it parallel to its length. The time period of each part, if the time period of the original magnet in the same field is T0​ , will be

T0​

2T0​​

4T0​​

4T0​