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Question

In a cylindrical water tank, there are two small holes Q and P on the wall at a depth of h1 and at a height of h2 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

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Solution

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

R1 = R2 = R

u1t1 = u2t2 −(i)

where,

u1 = velocity of efflux at Q = √2gh1 and

u2 = velocity of efflux at P = √2g(H – h2)

t1 = time of fall of water stream through Q = √2(H−h1)g

t2 = time of fall of the water stream through P = √2h2g

Putting these values in the equation (i), we get

(H – h1)h1 = (H – h2)h2

[H – (h1 + h2)][h1 –h2] = 0

H = h1 + h2 is irrelevant because the holes are at two different heights. Therefore, h1 = h2 and h1/h2 =1.


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