# The length, breadth and mass of two bar magnets are same but their magnetic moments are 3 M and 2 M respectively…

Q: The length, breadth and mass of two bar magnets are same but their magnetic moments are 3 M and 2 M respectively. These are joined pole to pole and are suspended by a string. When oscillated in a magnetic field of strength B, the time period obtained is 5 s. If the poles of either of the magnets are reversed, then the time period of the combination in the same magnetic field will be

(a) 2√2 s

(b) 5√5 s

(c) 1 s

(d) 3√3 s

Ans: (b)

Time Period $\displaystyle T = 2 \pi \sqrt{\frac{1}{M B}}$

$\displaystyle T = \propto \sqrt{\frac{1}{M }}$

Joining pole to pole means sum position, for which T1 = 5 s.

If T2 is time period for difference position, then

$\displaystyle \frac{T_2}{T_1} = \sqrt{\frac{M_1 + M_2}{M_1-M_2}}$

$\displaystyle \frac{T_2}{T_1} = \sqrt{\frac{3 M + 2 M}{3 M - 2 M}} = \sqrt{5}$

$\displaystyle T_2 = \sqrt{5} T_1 = 5 \sqrt{5} s$

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