Question

Figure source two holes in a white tank containing a liquid common the water streams coming out of these holes strike the ground at the same point the height of the liquid column in the tank is:

(a) 10 cm
(b) 8 cm
(c) 9.8 cm
(d) 980 cm

Answer 1

Hint: To solve this question one must know about the range formula, one can simply put the values in the formula and we will get the required solution. The main principle that is used here is Bernoulli's principle. According to Bernoulli's principle, a fluid's speed increases at the same time that its static pressure or potential energy decreases.

Formula used:
\[R=2\sqrt{h(H-h)}\]
where H is the height of the container or the height till which liquid is filled, and h is the height which hole has been made

Complete answer:
According to Bernoulli's theorem, the sum of a fluid's energy when it is moving is constant. Or, to put it another way, no energy is lost as a result of friction between the fluid layers. For perfect fluids, this theorem applies.

In this question, we’ll make use of the formula \[R=2\sqrt{h(H-h)}\] and we are given that the range is the same at both heights.

In the first case, the hole is at a height of 4 cm which means we’re given $h=4cm$. So, for this, the equation will become
$R=2\sqrt{4(H-4)}$…….. (i)

And in the second case, the hole is at a height of 6 cm which means we’re given $h=6cm$. So for this, the equation will become:
$R=2\sqrt{6(H-6)}$……… (ii)

According to the question, the range is the same in both cases. Therefore, equation (i) must be equal to equation (ii)
$2\sqrt{4(H-4)}=2\sqrt{6(H-6)}$

Or we can write it as
$\Rightarrow 4(H-4)=6(H-6)$
$\Rightarrow 4H-16=6H-36$
$\Rightarrow 2H=20$
$\therefore H=10cm$
Therefore the height of the liquid column in the container is 10cm.

Hence, the correct option is A. 10 cm

Note: Bernoulli’s principle is nothing but the consequence of the law of conservation of energy. The conservation of energy concept can be used to derive Bernoulli's principle. According to this, the total amount of energy present in a fluid at any given location along a streamline will be the same in a steady flow. An increase in fluid speed implies an increase in dynamic pressure even when all the energy is constant (kinetic energy). This occurs at the same time that the potential energy, which includes the static pressure and internal energy, decreases.