In a cylindrical water tank there are two small holes Q and P on the wall at a depth of h1 from the 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 strike the ground at the same point. The ratio of h1 and h2 is

Question

In a cylindrical water tank there are two small holes Q and P on the wall at a depth of h1 from the 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 strike the ground at the same point. The ratio of h1 and h2 is (A) 1 (B) 2 (C)  > 1 (D)  < 1

Tardigrade Admin · Accepted Answer

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

R_{1} = R_{2} = R

u_{1} t_{1} = u_{2} t_{2}

...(i)
where

u_{1} =

velocity of efflux at

Q = (2 g h_{1})

and

u_{2} =

velocity of efflux at

P = [2 g (H - h_{2})]

t_{1} =

time of fall of water stream through

Q

is

= \frac{2 ( H - h _{1} )}{g}

t_{2} =

time of fall of the water stream through

P = \frac{2 h _{2}}{g}

Putting these values is Eq. (i), we get

(H - h_{1}) h_{1} = (H - h_{2}) h_{2}

or

[H - (h_{1} + h_{2})] [h_{1} - h_{2}] = 0

H = h_{1} + h_{2}

is irrelevant because the holes are at two different heights.
Therefore,

h_{1} = h_{2}

or

h_{1} / h_{2} = 1

$1$

$2$

$> 1$

$< 1$

1

2

>1

<1

$1$

$2$

$> 1$

$< 1$