Question

In a large cylindrical water tank there are two small holes Q and P on the wall at a depth of h₁ from upper level of water and at a height of h₂ from the lower end of the tank respectively as shown in the figure. Water coming out from both the holes strikes the ground at the same point. The ratio of h₁ and h₂ is:

• A. 1
• B. 2
• C. >1
• D. <1

Answer 1

The correct option is A

1

The two streams strike at the same point on the ground,

$\Rightarrow R_1=R_2=R$
$\Rightarrow v_1{t}_1=v_2{t}_2$..........(1)
Where$v_1$ = velocity of efflux at $Q=\sqrt{2g{h}_1}$ and
$v_2$= velocity of the efflux at$P=\sqrt{2g(H-h_2)}$
$t_1$ = Time of fall of the water stream through$Q=\sqrt{\frac{2(H-h_2)}{g}}$
$t_2$= Time of fall of the water stream through P=$\sqrt{\frac{2h_2}{g}}$
Putting these values in equation (1), we obtain,
$(H-h_1)h_1=(H-h_2)h_2\Rightarrow [H-(h_1+h_2\left)\right][h_1-h_2]=0$
$\Rightarrow H-h_1+h_2$ is irrelevant because the holes are at two different heights, therefore $h_1=h_2$$\Rightarrow \frac{h_1}{h_2}=1$
Hence (A) is correct .