# A vibration magnetometer consists of two identical bar magnets placed one over the other such that they are perpendicular and bisect each other…

Q: A vibration magnetometer consists of two identical bar magnets placed one over the other such that they are perpendicular and bisect each other. The time period of oscillation in a horizontal magnetic field is 2(5/4) sec. One of the magnets is removed and if the other magnet oscillates in the same field, then the time period in seconds is:

(a) 2(1/4)

(b) 2(1/2)

(c) 2

(d) 2(3/4)

Ans: (c)

Sol: When two identical bar magnets are held perpendicular to each other.

$\displaystyle M_1 = \sqrt{M^2 + M^2}$

$\displaystyle M_1 = \sqrt{2} M$ ; I1 = I

T1 = 2(5/4) sec ; T2 = ?

M2 = M (as one magnet is removed)

I2 = I/2

$\displaystyle \frac{T_2}{T_1} = \sqrt{\frac{I_2}{I_1}\times \frac{M_1}{M_2}}$

$\displaystyle \frac{T_2}{T_1} = \sqrt{\frac{1}{2}\times \frac{\sqrt{2}M}{M}}$

$\displaystyle \frac{T_2}{T_1} = \frac{1}{2^{1/4}}$

$\displaystyle T_2 = \frac{T_1}{2^{1/4}}$

$\displaystyle T_2 = \frac{2^{5/4}}{2^{1/4}}$

T2 = 2 sec

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