Time period for a magnet is T. If it is divided in four equal parts along its axis and perpendicular to its axis as shown then time period for each part will be

Options

A. `4T`
B. `T//4`
C. `T//2`
D. `T`

Answer

C

Explanation

When magnet of length l is cut into four equal parts then
`m^(')=m/2 and l^(')=l/2, :. M^(')=m/2xxl/2=(ml)/4=M/4`
New moment of inertia
`I^(')=(wl^(2))/12=(w/4.(1/2)^(2))/12=1/16.(wl^(2))/12`
Here w is the mass of magnet.
`:. I^(')=1/16I`, Time period of each part
`T^(')=2pisqrt(I^(')/(M^(')B_(H)))`
`=2pisqrt((I//16)/((M//4)B_(H)))=2pisqrt(I/(4MB_(H)))=T/2`