Oscillating Ring!

Classical Mechanics Level 4

A disc of mass m m and radius R R is fastened with two rods of torsional constant 6 C 6C and 3 C 3C as shown. Time period of small oscillation of disc about it's axis in the left case and right case are respectively T 1 T_1 and T 2 T_2 .

What is the value of T 1 2 T 2 2 \large \frac{T_1^2}{T_2^2} is?

None of These 2 9 \frac{2}{9} 3 4 \frac{3}{4} 9 4 \frac{9}{4} 9 2 \frac{9}{2}

Nishant Rai by Nishant Rai , 25, India

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1 solution

The equivalent single torsional constant at LEFT is C 1 = 1 1 3 C + 1 6 C = 2 C . a t R I G H T i s C 2 = 3 C + 6 C = 9 C . T 1 2 ∗ C 1 = T 2 2 ∗ C 2 . ∴ T 1 2 T 2 2 = 9 2 . ~C_1=\dfrac 1 {\frac 1 {3C} +\frac 1 {6C} } =2C.\\at~~ RIGHT~~ is~~ C_2=3C+6C=9C.\\T_1^2*C_1=T_2^2*C_2.\\ \therefore~\dfrac{T_1^2}{T_2^2}=\color{#D61F06}{\dfrac 9 2}.

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