Question

A cylindrical vessel of $90\text{cm}$ height is filled upto the brim. It has four holes 1, 2, 3, 4 which are respectively at heights of $20\text{cm},30\text{cm},40\text{cm}$ and $50\text{cm}$ from the horizontal floor $PQ$. The water falling at the maximum horizontal distance from the vessel comes from

• A. Hole number 4
• B. Hole number 3
• C. Hole number 2
• D. Hole number 1

Answer 1

Answer: (A), (B)

The correct options are
A Hole number 4
B Hole number 3

In general, from Toricelli's theorem velocity of efflux $v=\sqrt{2gh}$ where $h$ is depth of hole from water surface.


Range of the water falling on surface PQ from a hole at a depth of $h$ below surface is
$R=v\sqrt{\frac{2(H-h)}{g}}$ (where $v=\sqrt{2gh}$)
$R=2\sqrt{h(H-h)}$


Now substituting $h$ for different holes

For Hole (1):
$H-h=20\text{cm},h=70\text{cm}$
$R_1=2\sqrt{70\left(20\right)\text{cm}}=20\sqrt{14}\text{cm}$
For Hole (2):
$H-h=30;h=60$
$R_2=2\sqrt{30\left(60\right)\text{cm}}=20\sqrt{18}\text{cm}$
For Hole (3):
$H-h=40;h=50$
$R_3=2\sqrt{40\left(50\right)\text{cm}}=20\sqrt{20}\text{cm}$
For Hole (4): $H-h=50;h=40$
$R_4=2\sqrt{50\left(40\right)\text{cm}}=20\sqrt{20}\text{cm}$
Thus
$R_4=R_3>R_2>R_1$

Options $A,B$ are correct