Simple Harmonic Motion Test

Result

Simple Harmonic Motion Test - 6

Score
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Rank
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TIME Taken - -

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Question 1
1 / -0

A hollow metallic sphere, filled with water, is hung from a support by a long thread. A small hole is made at the bottom of the sphere and it is oscillated. How will the time period of oscillations be affected as water slowly flows out of the hole?

A
The time period will remain unchanged as water is flowing out.

B
The time period will keep increasing until the sphere is empty.

C
The time period will keep decreasing until the sphere is empty.

D
The time period will increase at first, then decrease until the sphere is empty; finally the period will be the same as that when the sphere was full of water.

Solution

The length of the pendulum (I) is the distance between the point of support and the centre of mass of the sphere. The centre of mass (CM) of a sphere is at its centre when it is empty and completely filled with water. The CM falls below the centre of the sphere as the water flows out until the mass of the water becomes same as the mass of the sphere, after which CM will shift upward and the CM will return to its original value. Hence, the effective length of the pendulum (and hence, its time period) will increase, then decrease and when sphere is empty, then it becomes equal to the time period when the sphere was full of water. Thus, the correct choice is (4).