Consider a water tank as shown in the figure. It's cross-sectional area is $0.4 \mathrm{~m}^{2}$. The tank has an opening $B$ near the bottom whose crosssection area is $1 \mathrm{~cm}^{2}$. A load of $24 \mathrm{~kg}$ is applied on the water at the top when the height of the water level is $40 \mathrm{~cm}$ above the bottom, the velocity of water coming out the opening $B$ is $\mathrm{v} \mathrm{ms}^{-1}$. The value of $\mathrm{v}$, to the nearest integer, is____________. [Take value of $g$ to be $10 \mathrm{~ms}^{-2}$ ]
$\mathrm{m}=24 \mathrm{~kg}$
$\mathrm{~A}=0.4 \mathrm{~m}^{2}$
$\mathrm{a}=1 \mathrm{~cm}^{2}$
$\mathrm{H}=40 \mathrm{~cm}$
Using Bernoulli's equation
$=\mathrm{P}_{0}+0+\frac{1}{2} \rho \mathrm{v}^{2}$ .......(1)
$\Rightarrow$ Neglecting $\mathrm{v}_{1}$
$\Rightarrow \mathrm{v}=\sqrt{2 \mathrm{gH}+\frac{2 \mathrm{mg}}{\mathrm{A} \rho}}$
$\Rightarrow \mathrm{v}=\sqrt{8+1.2}$
$\Rightarrow \mathrm{v}=3.033 \mathrm{~m} / \mathrm{s}$
$\Rightarrow \mathrm{v} \simeq 3 \mathrm{~m} / \mathrm{s}$
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All Study Material
- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
- Electrostatics
- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
- Radioactivity
- Semiconductors
- Communication System
- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
- X-Rays
- All Subjects
- Physics
- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
- Waves
- Electric Charge and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Thermoelectric Effects of Electric Current
- Heating Effects of Electric Current
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Wave
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,