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A hole is made at the bottom of a tank filled with water (density $$=10^3 kg/m^3)$$. If the total pressure at the bottom of the tank is $$3 atm$$ ($$1 atm=10^5 N/m^2$$), then the velocity of efflux is


A
400m/s
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B
200m/s
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C
600m/s
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D
500m/s
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Solution

The correct option is B $$\sqrt {400}m/s$$
Applying Bernoulli's equation to two points one on the surface and the other just outside the hole at the bottom,
$$P_{atm} + \rho gh  + \dfrac{1}{2}\rho v^2 = P_{atm} + 0  + \dfrac{1}{2}\rho v'^2$$
Given,
$$ v=0$$
Pressure difference between top and bottom is $$2 atm$$ i.e equivalent of $$20m$$ of  water column
$$ \therefore h= 20$$

$$\dfrac{1}{2}\rho v'^2 = \rho gh$$

$$ \therefore \dfrac{1}{2} \times  1 \times  v'^2 =  10 \times  20$$

$$ \Rightarrow v' = \sqrt{400}$$

Physics

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