Question

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
liquid in the jar. Then the surface of jar is a
surface of revolution of the curve
​

Answer 1

n = 4

Explanation:

Let the height of liquid be denoted by y.

Given that dy/ dx = constant.

According to the equation of continuity, we get:

πx²(-dy/dx) = a√2gy

where a is the area of the hole at the bottom and g is gravity, both are constant.

√K . x² = √y

Squaring on both sides, gives you:

y = K.x^4

The surface of jar is a surface of revolution of the curve y=kx^n.

Comparing both, we find that n = 4.