Question

A small hole is made at the button of a symmetrical jar as shown in figure. 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

• A. $y=k{x}^4$
• B. $y=k{x}^2$
• C. $y=k{x}^3$
• D. $y=k{x}^5$

Answer 1

The correct option is A $y=k{x}^4$

Let $y=$ Height of liquid at any instant

Then, $\frac{dy}{dt}=$ Constant [ Given ]

From equation of continuity

$\pi x^2\left(\frac{-dy}{dx}\right)=a\sqrt{2gy}$

Since, Area of hole $\left(a\right)$, $\frac{dy}{dx}$ and $g$ are constant.

$\Rightarrow$ $\sqrt{k}{x}^2=\sqrt{y}$

Squaring both sides,

$\Rightarrow$ $k{x}^4=y$

$\therefore$ $y=k{x}^4$