A bar magnet of magnetic moment M and moment | vedclass

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

Question

(A) The time period of a bar magnet oscillating in a magnetic field $B$ is given by $T = 2 \pi \sqrt{\frac{I}{MB}}$.For the original magnet,$I = \frac

Vedclass · Accepted Answer

$T/2$

Vedclass · Answer

(A) The time period of a bar magnet oscillating in a magnetic field $B$ is given by $T = 2 \pi \sqrt{\frac{I}{MB}}$.For the original magnet,$I = \frac{m l^2}{12}$,where $m$ is the mass and $l$ is the length.When the magnet is cut into two equal pieces perpendicular to its length,the length of each piece becomes $l' = l/2$ and the mass becomes $m' = m/2$.The new moment of inertia $I'$ for each piece about its center is $I' = \frac{m' (l')^2}{12} = \frac{(m/2) (l/2)^2}{12} = \frac{m l^2}{12 	imes 8} = \frac{I}{8}$.The new magnetic moment $M'$ for each piece is $M' = M/2$.The new time period $T'$ is $T' = 2 \pi \sqrt{\frac{I'}{M' B}} = 2 \pi \sqrt{\frac{I/8}{(M/2) B}} = 2 \pi \sqrt{\frac{1}{4} \frac{I}{MB}} = \frac{1}{2} \left( 2 \pi \sqrt{\frac{I}{MB}} ight) = \frac{T}{2}$.

Similar Questions

Two magnets of same size and mass make respectively $10$ and $15$ oscillations per minute at a certain place. The ratio of their magnetic moments is

The time period of a magnet is $2 \, s$. The horizontal component of the Earth's magnetic field is $H$. When an external magnetic field $F$ is applied in the same direction,the new time period becomes $1 \, s$. What is the ratio $H/F$?

$A$ tangent galvanometer has $80$ turns of wire. The internal and external diameters of the coil are $19 \, cm$ and $21 \, cm$ respectively. The reduction factor of the galvanometer at a place where $H = 0.32 \, \text{oersted}$ will be $(1 \, \text{oersted} = 80 \, A/m)$.

The magnetic needle of a tangent galvanometer is deflected at an angle $30^{\circ}$ due to a magnet. The horizontal component of the earth's magnetic field is $0.34 \times 10^{-4} \text{ T}$,which is along the plane of the coil. The magnetic field due to the magnet is:

$A$ bar-magnet of moment of inertia $49 \times 10^{-2} \,kg-m^2$ vibrates in a magnetic field of induction $0.5 \times 10^{-4} \,T$. The time period of vibration is $8.8 \,s$. The magnetic moment of the bar magnet is (in $\,A-m^2$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module