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Question

Two identical rods each of mass m and length L, are joined and then suspended in a vertical plane so as to oscillate freely about an axis normal to the plane of paper passing through 'S' (point of suspension). Find the time period of such small oscillations.
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A
2π17L12g
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B
2π13L18g
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C
2π17L18g
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D
2π17L15g
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Solution

The correct option is C 2π17L18g

we know that time period of a physical pendulum is given by
T=2πIsupportmglcmIsupport=I1+I2=13mL2+(112mL2+mL2)=1712mL2lcm=3L4
T=2π     (1712mL2)(2m)g(3L4)=2π17L18g


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