Question

A liquid is coming out from the two orifices of a fully
filled tank kept on ground and falls on the same
horizontal distance. If one orifice is X1 above the
mid-point of the tank and other is x2 below the
mid-point of the tank. Then choose the correct
relation between X1 and x2
(1) X1 = x2
42) x2 = 221
(3) X1 = 2x2
(4) X1 = 4x2​

Answer 1

Answer:

The correct relation between x1 and x2 is

x1 = x2

Explanation:

A small hole is made of the side wall of the container such that its height from the ground is y while distance from free surface of top is x

now the speed of efflux of liquid coming out of the hole is given as

$v = \sqrt{2gx}$

now time taken by liquid to hit the ground

$t = \sqrt{\frac{2y}{g}}$

so the horizontal distance of liquid where it will hit the floor

$R = v t$

$R = 2\sqrt{xy}$

so here let the mid point is at height h from the base of the container

so here we have

$y = h + x_1$

$x = h - x_1[tex]</p><p>[tex]R_1 = 2\sqrt{(h + x_1)(h - x_1)}$

while for other hole we have

$y = h - x_2$

$x = h + x_2$

now the range is given as

$R_2 = 2\sqrt{(h - x_2)(h + x_2)}$

since we know that

$R_1 = R_2$

so we will have

$x_1 = x_2$

#Learn

Topic : Velocity of efflux

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