Time Period of Torsional pendulum case - (Formula)

T=2\pi \sqrt{\frac{I}{K}}

I= moment of inertia

K= torsional constant

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Question

In a pendulum bar magnet is osciallating in the magnetic field with time period  'T' if its mass is increased by four times then its time period will be

 Your Option is correct !!

A.

4T

B.

2T

C.

T

D.

\frac{T}{}2

Answers (1)
S Sayak

By changing only the mass of the bar magnet we only change the moment of inertia and not the torsional constant as that depends on the magnetization of the magnet and the magnetic field

Moment of inertia of rod of mass M and length L = I1 =\frac{ML^{2}}{12}

Time period of rod of mass M and length L = T = 2\pi \sqrt{\frac{I_{1}}{k}}

Moment of inertia of rod of mass 4M and length L= I2 = \frac{4ML^{2}}{12}=\frac{ML^{2}}{3} = 4I1

Time period of rod of mass M and length L = T'

\\T'=2\pi \sqrt{\frac{I_{2}}{k}}\\ T'=2\pi \sqrt{\frac{4I_{1}}{k}}\\ T'=4\pi \sqrt{\frac{I_{1}}{k}}\\ T'=2T

The new time period will be 2T.

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