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Question

Consider the following data and choose the correct option.

1. The time period of a simple pendulum, whose bob is a hollow metallic sphere is T.
2. The time period of a simple pendulum is T1, when the bob is filled with sand,
3. The time period of a simple pendulum is T2, when it is filled with mercury and
4. The time period of a simple pendulum is T3, when it is half-filled with mercury as shown.



A
T=T1=T2>T3
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B
T1=T1=T3>T
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C
T>T3>T1=T2
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D
T=T1=T2<T3
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Solution

The correct option is D T=T1=T2<T3
Time period of a pendulum doesnot depend upon mass, but it depends upon length (distance between point of suspension and centre of mass)
In first 3 cases, distance between point of suspension and centre of mass are same.
So, T=T1=T2,
In last case, when mercury is filled half of the bob, the distance between point of suspension and centre of mass is more than in previous cases.
So, T3 will be more than in other cases.
Hence 'D' is the correct option.

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