Question

A tank, which is open at the top, contains a liquid up to a height $H$. A small hole is made in the side of the tank at a distance $y$ below the liquid surface. The liquid emerging from the hole lands at a distance $x$ from the tank. Which of the following is not correct?

• A. The maximum value of $x$ is $H$.
• B. $x$ is maximum for $y=\frac{H}{2}$.
• C. If $y$ is increased from zero to $H$,$x$ will first increase and then decrease.
• D. The maximum value of $x$ will depend on the density of the liquid.

Answer 1

The correct option is D The maximum value of $x$ will depend on the density of the liquid.

The velocity of efflux $=v=\sqrt{2gy}$.
The emerging liquid moves as a projectile and reaches the ground in time $t$, where,
$H-y=\frac{1}{2}g{t}^2$ or $t=\sqrt{\frac{2(H-y)}{g}}$
$\therefore x=vt=2\sqrt{(H-y)y}.$
For $x$ to be maximum, $\frac{dx}{dy}=0$ or $y=\frac{H}{2}$
$\therefore x_{max}=H$.
$\therefore$ The expression of $x$ doesn’t contain the density term and so incorrect statement is (d)