A small hole is made at the bottom of a symmetrical jar as shown in figure. A liquid is filled into the jar upto a certain height. The rate of descension of liquid is independent of the level of the liquid in the jar. Then the surface of the jar is a surface of revolution of the curve -

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Let y be the height of the liquid at some instant. Then − dt dy ​ = constant (given). From the equation of continuity, ( π x 2 ) ( − d t d y ​ ) = a 2 g y ​ ( a = area of hole). Here, π ( d t − d y ​ ) , a , and g are constants. Hence, squaring the equation, we get y = k x 4 .

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