The length of a magnet is large compared to its width and breadth. The time period of its oscillation in a vibration magnetometer is ` 2 s`. The magnet is cut along its length into three equal parts and these parts are then placed on each other with their like poles together . The time period of this combination will be

Options

A. `2s`
B. `2/3 s`
C. `2sqrt3s`
D. `2//sqrt3s`

Answer

B

Explanation

The time period of oscillations of magnet
`T=2pisqrt(((I)/(MH)))" ".......(i)`
where I= moment of inertia of magnet
`=(mL^(2))/(12)` (m, being the mass of magnet)
M= pole strength `xx`L
and H = horizontal component of earth's mangetic field.
When the there equal parts of magnet are placed on one another with their like poles together, then
`I'(1)/(12)((m)/(3))xx((L)/(3))xx3`
`=(1)/(12)(mL^(2))/(9)=(I)/(9)`
and M'= pole strength `xx(L)/(3)xx3=M`
Hence, T' `=2pisqrt(((I//9)/(MH)))`
`impliesT'=(1)/(3)xxT`
`T'=(2)/(3)s`