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

Options

A. `y=kx^(4)`
B. `y=kx^(2)`
C. `y=kx^(3)`
D. `y=kx^(5)`

Answer

A

Explanation

Let `y` the height of liquid at same instant then `(a="area of hole"(-dy)/(dt)="constant given")`
`asqrt(2gy)=pix^(2)(-(dy)/(dt))`
`pi,((-dy)/(dt))` and g are constant
squaring the equation we get `y=kx^(4)`