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 $2^{2/5}$s. One of the magnets is removed and if the other magnet oscillates in the same field , then the time period in second is
A) $2^{1/4}$
B) $2^{1/2}$
C) 2
D) 4
Explanation
(c) When two identical bar magnets are held perpendicular to each other.
$M_{1} = \sqrt{M^{2} + M^{2}} = M\sqrt{2},I_{1} = I$
$T_{1} = 2^{5/4\ }s,T_{2} = ?$
$M_{2} = M$(as one magnet is removed)
$I_{2} = I_{1}/2$
$\frac{T_{2}}{T_{1}} = \sqrt{\frac{I_{2}}{M_{2}}\frac{M_{1}}{I_{1}} =}\sqrt{\frac{1}{2}.\frac{M\sqrt{2}}{M}} = \left( \frac{1}{\sqrt{2}} \right)^{1/2}$
$= \frac{1}{2^{1/4}}$
$T_{2} = T_{1} \times \frac{1}{2^{1/4}} = 2^{5/4} \times \frac{1}{2^{1/4}} =$2s
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.