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A hollow sphere is filled up with water and is suspended using a long string. As water trickels out slowly through an orifice at the lower part of the sphere, it is observed that the time period of the pendulum first increases and later continues to decrease. Explain these observations.

Answer» <html><body><p></p><a href="https://interviewquestions.tuteehub.com/tag/solution-25781" style="font-weight:bold;" target="_blank" title="Click to know more about SOLUTION">SOLUTION</a> :Time period of a simple pendulum at a <a href="https://interviewquestions.tuteehub.com/tag/fixed-457597" style="font-weight:bold;" target="_blank" title="Click to know more about FIXED">FIXED</a> place is directly proportional to the <a href="https://interviewquestions.tuteehub.com/tag/square-650836" style="font-weight:bold;" target="_blank" title="Click to know more about SQUARE">SQUARE</a> root of the effective length of the pendulum. Distance between the point of suspension and the centre of gravity of the bob is the effective length. Time period of oscillation increases or decreases with the increase or decrease of its effective length. <br/> Centre of gravity of the spherical bob, completely, filled with water, lies at the centre of the sphere. As water trickles out through the orifice, the <a href="https://interviewquestions.tuteehub.com/tag/upper-721698" style="font-weight:bold;" target="_blank" title="Click to know more about UPPER">UPPER</a> <a href="https://interviewquestions.tuteehub.com/tag/part-596478" style="font-weight:bold;" target="_blank" title="Click to know more about PART">PART</a> of the sphere starts getting emptied making the lower half heavier than the upper half. As a result, the centre of gravity of the bob starts going down from the centre of the sphere and the effective length begins to increase. Time period also starts increasing. When more water trickles out, the centre of gravity of the bob again starts shifting towards the centre of the sphere resulting in a decrease in the effective length, and consequently, lowering of the time period. When the hollow sphere becomes completely empty, the centre of gravity shifts back to the centre of the sphere and the effective length regains its initial value. As a result, the final value of the time period equals its initial value.</body></html>


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