The magnetic needle of a vibration magnetomet | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The frequency of oscillation $n$ of a vibration magnetometer is given by $n = \frac{1}{2 \pi} \sqrt{\frac{M H}{I}}$, which implies $n \propto \sqr

Vedclass · Accepted Answer

$\sqrt{63}$

Vedclass · Answer

(B) The frequency of oscillation $n$ of a vibration magnetometer is given by $n = \frac{1}{2 \pi} \sqrt{\frac{M H}{I}}$, which implies $n \propto \sqrt{B_{net}}$.In the first case, the net magnetic field is $H$. So, $n_1 = 12 \propto \sqrt{H}$.In the second case, the bar magnet is placed along the axis, so the net field is $H + H_1$. Thus, $n_2 = 15 \propto \sqrt{H + H_1}$.Taking the ratio: $\frac{15}{12} = \sqrt{\frac{H + H_1}{H}} \Rightarrow \frac{5}{4} = \sqrt{1 + \frac{H_1}{H}} \Rightarrow \frac{25}{16} = 1 + \frac{H_1}{H} \Rightarrow \frac{H_1}{H} = \frac{9}{16}$.When the poles are interchanged, the field becomes $H - H_1$. Let the new frequency be $n_3$.$\frac{n_3}{n_1} = \sqrt{\frac{H - H_1}{H}} = \sqrt{1 - \frac{H_1}{H}} = \sqrt{1 - \frac{9}{16}} = \sqrt{\frac{7}{16}} = \frac{\sqrt{7}}{4}$.Therefore, $n_3 = 12 	imes \frac{\sqrt{7}}{4} = 3 \sqrt{7} = \sqrt{9 	imes 7} = \sqrt{63}$ oscillations per minute.

Similar Questions

The tangent galvanometer,when connected in series with a standard resistance,can be used as:

$A$ dip circle lies initially in the magnetic meridian,it shows an angle of dip $\delta$ at a place. The dip circle is rotated through an angle $\alpha$ in the horizontal plane and then it shows an angle of dip $\delta^{\prime}$. Hence $\frac{\tan \delta^{\prime}}{\tan \delta}$ is

$A$ thin magnetic iron rod of length $30 \ cm$ is suspended in a uniform magnetic field. Its time period of oscillation is $4 \ s$. It is broken into three equal parts. The time period in seconds of oscillation of one part when suspended in the same magnetic field is

If a brass bar is placed on a vibrating magnet, then its time period

Vedclass Test Series

Exam Paper Generator

Online Exam Module