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 fall 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 y = kxn, the value of n is :

Engineering

Physics

Liquid Pressure

Calculus

BernoulIis Equation and Equation of Continuity

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 fall 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 y = kxⁿ, the value of n is :

LiveFree JEE Main Previous Year Online Papers Live Free JEE Advance Previous Year Online Papers

College PredictorLive

Know your College Admission Chances Based on your Rank/Percentile, Category and Home State.

Get your JEE Main Personalised Report with Top Predicted Colleges in JoSA

Let height of liquid in the jar decreases at rate dy/dt and A = px2 be the cross-sectional area of liquid at time t. Then
A $(\frac{- dy}{dt})$ = av
πr² $(- \frac{dy}{dt})$ = a $\sqrt{2 gy}$
πr² $(- \frac{dy}{dt})$ = a $\sqrt{2 {gkx}^{n}}$ ( $∵$ y = kxn)
(dy/dt) will be independent of x, if tern containing x gets concelled out. Thus,
2 = $\frac{n}{2}$ ⇒ n = 4