The length of a magnet is large compared to i | vedclass

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

Question

(B) The time period of oscillation of a magnet is given by $T = 2 \pi \sqrt{\frac{I}{MH}}$,where $I$ is the moment of inertia,$M$ is the magnetic mome

Vedclass · Accepted Answer

$2 / 3 ~s$

Vedclass · Answer

(B) The time period of oscillation of a magnet is given by $T = 2 \pi \sqrt{\frac{I}{MH}}$,where $I$ is the moment of inertia,$M$ is the magnetic moment,and $H$ is the horizontal component of the Earth's magnetic field.For the original magnet of mass $m$ and length $L$,$I = \frac{mL^2}{12}$ and $M = q_m L$ (where $q_m$ is pole strength).When the magnet is cut into three equal parts along its length,each part has mass $m' = m/3$,length $L' = L/3$,and pole strength $q_m' = q_m$.When these three parts are stacked together with like poles aligned,the new moment of inertia $I'$ is the sum of the moments of inertia of the three parts: $I' = 3 	imes \frac{m'(L')^2}{12} = 3 	imes \frac{(m/3)(L/3)^2}{12} = \frac{mL^2}{12 	imes 9} = \frac{I}{9}$.The new magnetic moment $M'$ is the sum of the magnetic moments of the three parts: $M' = 3 	imes (q_m 	imes L/3) = q_m L = M$.The new time period $T'$ is $T' = 2 \pi \sqrt{\frac{I'}{M'H}} = 2 \pi \sqrt{\frac{I/9}{MH}} = \frac{1}{3} 	imes 2 \pi \sqrt{\frac{I}{MH}} = \frac{T}{3}$.Given $T = 2 ~s$,therefore $T' = 2/3 ~s$.

Column-$I$	Column-$II$
$(a)$ Gymnosperms	$(p)$ Trimerous flowers
$(b)$ Monocots	$(q)$ Absence of flowers
$(c)$ Dicots	$(r)$ Primitive flowers
$(d)$ Pteridophytes	$(s)$ Tetramerous or pentamerous flowers

Similar Questions

Which of the following are found in extreme saline conditions?

Which one of the following is not a calcination reaction?

Which among the following is a dicarboxylic acid?

Match the following columns:

Column-$I$ Column-$II$

$(a)$ Gymnosperms $(p)$ Trimerous flowers

$(b)$ Monocots $(q)$ Absence of flowers

$(c)$ Dicots $(r)$ Primitive flowers

$(d)$ Pteridophytes $(s)$ Tetramerous or pentamerous flowers

Vedclass Test Series

Exam Paper Generator

Online Exam Module