Question

A rectangular tank is placed on a horizontal ground end is filled with water to a height $H$ above the base. A small hole is made on one vertical side at a depth $D$ below the level of water in the tank. The distance $x$ from the bottom of the tank, at which the water jet from the tank will hit the ground is,

• A. $2\left[D\right(H-D\left)\right]{]}^{1/2}$
• B. $2(gD{)}^{\frac{1}{2}}$
• C. $2\left[D\right(H+D\left)\right]{]}^{1/2}$
• D. $\frac{1}{2}(DH{)}^{\frac{1}{2}}$

Answer 1

The correct option is A $2\left[D\right(H-D\left)\right]{]}^{1/2}$

Time taken by liquid drop to fall

$S=ut+\frac{1}{2}{at}^2$

$t=\sqrt{\frac{2(H-D)}{g}}$

Horizontal velocity of liquid $=\sqrt{2gD}$

Range $=\sqrt{\frac{2(H-D)}{g}}\times \sqrt{2gD}$

Range $=2\sqrt{D(H-D)}$