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Question

What is the period of a pendulum formed by pivoting a meter stick so that it is free to rotate about a horizontal axis passing through the 75 cm mark?


A
1.00 sec
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B
1.25 sec
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C
1.53 sec
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D
2.5 sec
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Solution

The correct option is C 1.53 sec

Let m be the mass and l be the length of the stick.
l=100 cm
The distance of the point of suspension from centre of gravity is d=25 cm
Moment of inertia about a horizontal axis through O is
I=IC+md2I=ml212+md2
Now, time period for physical pendulum is
T=2πImgd=2π  ml212+md2mgd
T=2πl2+12d212 gd=2π12+12(0.25)212×9.8×0.25=1.53 s

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