The magnetic moments of two bar magnets of same size are in the ratio `1:2.` When they are placed one over the other with their similar poles together, then their perlod of oscillation in a magnetic field is 3s. If one of the magnets is reversed, then the period of oscillation in the same field will be q

Options

A. 2s
B. `2 sqrt3 s `
C. `2 sqrt2 s`
D. `2sqrt5 s`

Answer

B

Explanation

Time period of a bar magnet suspended in uniform magnetic field is given by the following relation.
` T = 2pi sqrt( (l)/(MB) )`
Here I is moment of inertia of magnet. Here in both the cases magnetic field intensity remains the same and on reversing the magnet moment of inertia is also not affected. Hence we can say that time period of oscillation is inversely proportional to the square root of magnetic moment of magnet. If `T_1` and `T_2` are the time period of oscillations in two cases then we can write the following:
`(T_1^2)/(T_2^2) = M_2/M_1` ...(i)
Let M is magnetic moment of one bar magnet then magnetic moment of the other can be assumed to be 2M, because given ratio is 1:2. In first case both the magnets are similarly directed hence net magnetic moment can be written as follows:
`M_1` = 2M + M = 3M
`M_2` =2M - M=M
Substituting above value in equation (1) we get the following:
` (T_1^2)/(T_2^2) = M_2/M_1 rArr (2^2)/(T_2^2) = (M)/(3M)`
` rArr T_2^2 = 12`
` rArr T_2 = 2 sqrt3 s`