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  • What is the frequency of a torsional pendulum in which the disc is having mass of 2 Kg and radius = 30 cm. The torsional stiffnness of the the wire through which the disc is hanged with the ceiling

What is the frequency of a torsional pendulum in which the disc is having mass of 2 Kg and radius = 30 cm. The torsional stiffnness of the the wire through which the disc is hanged with the ceiling is 20 N-m ? ( Answer will be in Hz)

Option: 1

2.4


Option: 2

2


Option: 3

4


Option: 4

4.8


Answers (1)

best_answer

 

 

The Time Period of the Torsional pendulum is given as 

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

where 

I= moment of inertia

k= torsional constant

As, 

 T=2\pi \sqrt{\frac{I}{k}}

So, the frequency is   

 f = \frac{1}{T} = \frac{1}{2 \pi}\sqrt{\frac{k}{I}}

\\ f = \frac{1}{2 \pi}\sqrt{\frac{20}{I}} \\ \\ So,I=\frac{1}{2}M.R^2 = \frac{1}{2} \times 2 \times (0.3)^2 \\ \\ I = 0.09 \ Kg-m^2 \\ \\ So, \ f = \frac{1}{2 \pi}.\sqrt{\frac{20}{0.09}} = 2.4 \ Hz

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Riya

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