The time period of a freely suspended magnet is 4 seconds. If it is broken in length into two equal parts and one part is suspended in the same way, then its time period will be

Options

A. 4 sec
B. 2 sec
C. 0.5 sec
D. 0.25 sec

Answer

B

Explanation

`T = 2pi sqrt(1/(MB)) = 4` sec
When magnet is cut into two equal parts, the magnetic moments
`M' = M/2`
New moment of inertia `I' = ((omega//2)(l//2)^(2))/12 = 1/8 xx (omega t^(2))/12`
W = initial mass of the magnet.
But, `I = (omega l^(2))/12, therefore I' = 1/8`
`therefore` New time period `T' = 2pi sqrt(I^(')/(MB_(H)))`
`T' = 2pi sqrt((1//8)/((M//2)B_(H))) rArr 1/2 xx 2pi sqrt(1/(MH))`
`=1/2 xx T = 1/2 xx 4 = 2` sec