The water filled pendulum

Classical Mechanics Level 2

A simple pendulum with a weightless string has a bob that is filled with water. If a hole is made at the bottom of the bob and the water starts leaking out, what will happen to the time period of the pendulum?

Hint: Time period is directly proportional to the distance between the point of suspension and center of mass of the bob.

Image credit: Wikipedia Fizped
Remains the same Increases Initially decreases then comes back to the original value Initially increases then comes back to the original value

Siddharth Gopujkar by Siddharth Gopujkar , 30, India

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3 solutions

Subham Gupta
Jun 25, 2014

Time period is directly proportional to the root of distance between point of suspension of string and center of mass of the bob. Now when the water leaks its level falls and the net COM falls downwards thereby increasing the distance. After the water is completely leaked out, the COM comes back to original position. Hence T first increases and then comes back to original value.

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Subham is right. When the water level goes down, it's Center of Mass (CM) goes down and so does that of the bob. When all the water is out, the CM comes back to it's original position.

Siddharth Gopujkar - 6 years, 11 months ago

what is COM?

Apurv Rajput - 6 years, 11 months ago

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Center of Mass (maybe)

Johan Setiawan - 6 years, 11 months ago

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Yup! The hint gave the answer.

Satvik Golechha - 6 years, 11 months ago

Made a silly mistake Easy question

Ankur Manna - 6 years, 10 months ago
Pranay Pratyush
Jun 28, 2014

Take the bob and water as 2 different bodies. The COM of the system would be taken as the result of both of them. When water leaks out the COM of water body falls, but since the mass of water body is also decreasing so its contribution in COM will also decrease. Therefore after a critical water mass the COM again starts to rise, till all the water has leaked and the COM is at centre again. SO THE COM STARTS FROM CENTRE GOES TO A CRITICAL LEVEL BELOW CENTRE THE RISES BACK TO CENTRE. ALSO the time period is directly proportional to the root of length (approximately (but we can always say that it will increase if length increases)). So time period increases and then stops increasing at a certain time, then decreases and comes to the original value.

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Jaivir Singh
Jun 27, 2014

INITIALLY DISTANCE BETWEEN SUSPENSION POINT AND COM INCREASES THEN FINALLY BECOMES EQUAL TO INITIAL LENGTH

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