JEE Main 202118 MarchEvening Shift

Exam: JEE Main
Year: 2021
Date: 18 March
Shift: Evening Shift
Subject: Physics
Chapter: Mechanical Properties of Fluids

JEE Main 2021 · 18 March · Evening Shift · Physics · Mechanical Properties of Fluids

Consider a water tank as shown in the figure. It's cross-sectional...

Consider a water tank as shown in the figure. It's cross-sectional area is $0 . 4{m}^{2}$ . The tank has an opening $B$ near the bottom whose cross-section area is $1{cm}^{2}$ . A load of $24kg$ is applied on the water at the top when the height of the water level is $40cm$ above the bottom, the velocity of water coming out the opening $B$ is $vm{s}^{- 1}$ . The value of $v$ , to the nearest integer, is ___ .[Take the value of $g$ to be $10{ms}^{- 2}$ ]

Consider a water tank as shown in the figure. It's cross-sectional area is 0 . 4 m ^ 2 . The tank has an opening B near

Correct answer

Step-by-step solution

Consider a water tank as shown in the figure. It's cross-sectional area is 0 . 4 m ^ 2 . The tank has an opening B near

$m = 24kg$

$A = 0 . 4{m}^{2}$

$a = 1{cm}^{2}$

$H = 40cm$

Using Bernoulli's equation,

$⇒ \left({P}_{0} + \dfrac{mg}{A}\right) + ρgH + \dfrac{1}{2}P{v}_{1}^{2}$

$= {P}_{0} + 0 + \dfrac{1}{2}ρ{v}^{2} . . . \left(1\right)$

$⇒$ Neglecting ${v}_{1}$

$⇒ v = \sqrt{2gH + \dfrac{2mg}{Aρ}}$

$⇒ v = \sqrt{8 + 1 . 2}$

$⇒ v = 3 . 033m{s}^{- 1}$

$⇒ v ≃ 3m{s}^{- 1}$

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