A small circular loop of conducting wire has radius a and carries… - Vidyadip

MCQ

A small circular loop of conducting wire has radius $a$ and carries current $I$. It is placed in a uniform magnetic field $\mathrm{B}$ perpendicular to its plane such that when rotated slightly about its diameter and released, it starts performing simple harmonic motion of time period $T$. If the mass of the loop is $m$ then

A
$\mathrm{T}=\sqrt{\frac{\pi \mathrm{m}}{2 \mathrm{IB}}}$
B
$\mathrm{T}=\sqrt{\frac{2 \pi \mathrm{m}}{\mathrm{IB}}}$
C
$\mathrm{T}=\sqrt{\frac{\pi \mathrm{m}}{\mathrm{IB}}}$
D
$\mathrm{T}=\sqrt{\frac{2 \mathrm{m}}{\mathrm{IB}}}$

✓

Answer

$\overrightarrow{\mathrm{T}}=\overrightarrow{\mathrm{M}} \times \overrightarrow{\mathrm{B}}=-\mathrm{MB} \sin \theta$

$\mathrm{I} \alpha=-\mathrm{MB} \sin \theta$

for small $\theta$

$\alpha=-\frac{\mathrm{MB}}{\mathrm{I}} \theta$

$\omega=\sqrt{\frac{\mathrm{MB}}{\mathrm{I}}}=\sqrt{\frac{(\mathrm{I})\left(\pi \mathrm{R}^{2}\right) \mathrm{B}}{\left(\frac{\mathrm{mR}^{2}}{2}\right)}}$

$\omega=\sqrt{\frac{2 \mathrm{I} \pi \mathrm{B}}{\mathrm{m}}}$

$\therefore \mathrm{T}=\frac{2 \pi}{\omega}=\sqrt{\frac{2 \pi \mathrm{m}}{\mathrm{IB}}}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "MCQ" from Magnetic Effect of Current→Magnetic Effect of Current — all question types→JEE physics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

The path of a projectile in the ${ }^0$ absence of air drag is shown in the figure by dotted line. If the air resistance is not ignored then which one of the path shown in the figure is appropriate for the projectile

In terms of Rydberg's constant $R$, the wave number of the first Balmer line is

A particle starts from rest. Its acceleration versus time $(t)$ is as shown in the figure. The maximum speed of the particle will be

The efficiency of transformer is very high because

A train moves towards a stationary observer with speed $34 \mathrm{~m} / \mathrm{s}$. The train sounds a whistle and its frequency registered by the observer is $f_1$. If the train's speed is reduced to $17 \mathrm{~m} / \mathrm{s}$, the frequency registered is $f_2$. If the speed of sound is $340 \mathrm{~m} / \mathrm{s}$ then the ratio $f_1 / f_2$ is

Which of the following law states that "good absorbers of heat are good emitters"

A stone is dropped into a lake from a tower $500$ metre high. The sound of the splash will be heard by the man approximately after

The dimension of the ratio of angular to linear momentum is

Correct relation for triode is

A galvanometer of $100 \Omega$ resistance gives full scale deflection when $10 \mathrm{~mA}$ of current is passed. To convert it into $10 \mathrm{~A}$ range ammeter, the resistance of the shunt required will be