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JEE Main 20199 JanuaryEvening Shift
Exam
JEE Main
Year
2019
Date
9 January
Shift
Evening Shift
Subject
Physics
Chapter
Mechanical Properties of Fluids

JEE Main 2019 · 9 January · Evening Shift · Physics · Mechanical Properties of Fluids

The top of a water tank is open to air and its water level is...

The top of a water tank is open to air and its water level is maintained. It is giving out 0.74m30.74{m}^{3} water per minute through a circular opening of 2cm2cm radius in its wall. The depth of the centre of the opening from the level of water in the tank is close to:The top of a water tank is open to air and its water level is maintained. It is giving out 0.74 m ^ 3 water per minute

Options

  1. A2.9m2.9m
  2. B4.8m4.8m
  3. C6.0m6.0m
  4. D9.6m9.6m

Correct answer

B. 4.8m4.8m

Step-by-step solution

The top of a water tank is open to air and its water level is maintained. It is giving out 0.74 m ^ 3 water per minute

Volume of water flowing out=Av= Av, where AA is area of opening and vv is speed of water from the opening.

Volume=πr2v\text{Volume} = \pi{r}^{2}v

0.74(m3min⁡)=(3.14×(2×10−2)2×2×10×H)m3s×60smin⁡0 . 74\left(\dfrac{{m}^{3}}\min\right) = \left(3.14 \times {\left(2 \times {10}^{- 2}\right)}^{2} \times \sqrt{2 \times 10 \times H}\right)\dfrac{{m}^{3}}{s} \times \dfrac{60s}\min

⇒H=(0.7460×3.14×4×10−4)2×120⇒ H = {\left(\dfrac{0.74}{60 \times 3.14 \times 4 \times {10}^{- 4}}\right)}^{2} \times \dfrac{1}{20}

⇒H=4.8m⇒ H = 4.8m

Hence, the height of water in the tank was 4.8m4 . 8m from the bottom of the tank.

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