(D) For the first hole at depth $h/2$ in the liquid of density $\rho$:Using Torricelli's law,$v_1 = \sqrt{2g(h/2)} = \sqrt{gh}$.For the second hole at

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(D) For the first hole at depth $h/2$ in the liquid of density $\rho$:Using Torricelli's law,$v_1 = \sqrt{2g(h/2)} = \sqrt{gh}$.For the second hole at depth $3h/2$ from the surface,it is at a depth $h/2$ within the liquid of density $2\rho$:Applying Bernoulli's theorem between the top surface and the second hole:$P_0 + \rho gh + 2\rho g(h/2) = P_0 + \frac{1}{2}(2\rho)v_2^2$$\rho gh + \rho gh = \rho v_2^2$$2\rho gh = \rho v_2^2$$v_2 = \sqrt{2gh}$.Now,calculating the ratio:$\frac{v_1}{v_2} = \frac{\sqrt{gh}}{\sqrt{2gh}} = \frac{1}{\sqrt{2}}$.

Class 11 Physics Mechanical Properties of Fluids Velocity of Efflux and Torricelli's law

Difficult

Equal volumes of two immiscible liquids of densities $\rho$ and $2\rho$ are filled in a vessel as shown in the figure. Two small holes are punched at depths $h/2$ and $3h/2$ from the surface of the lighter liquid. If $v_1$ and $v_2$ are the velocities of efflux at these two holes,then $v_1/v_2$ is:

A
$\frac{1}{2\sqrt{2}}$
B
$\frac{1}{2}$
C
$\frac{1}{4}$
D
$\frac{1}{\sqrt{2}}$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Physics Questions

Chapter

Mechanical Properties of Fluids

Subtopic

Velocity of Efflux and Torricelli's law

$A$ large open tank has two holes in the wall. One is a square hole of side $L$ at a depth $y$ from the top and the other is a circular hole of radius $R$ at a depth $4y$ from the top. When the tank is completely filled with water, the quantities of water flowing out per second from the two holes are the same. Then the value of $R$ is

DifficultTS EAMCET 2011

View Solution

$A$ large storage tank, open to the atmosphere at the top and filled with water, develops a small hole in its side at a point $20.0 \ m$ below the water level. If the rate of flow from the hole is $3.08 \times 10^{-5} \ m^3 s^{-1}$, then the diameter of the hole is (Take $g = 10 \ m s^{-2}$): (in $mm$)

MediumTS EAMCET 2022

View Solution

$A$ tank with vertical walls is mounted so that its base is at a height $H$ above the horizontal ground. The tank is filled with water to a depth $h$. $A$ hole is punched in the side wall of the tank at a depth $x$ below the water surface. To have maximum range of the emerging stream,the value of $x$ is

MediumAP EAMCET 2001

View Solution

$A$ wide vessel with a small hole at the bottom is filled with two liquids. The density and height of one liquid are $\rho_1$ and $h_1$ and that of the other are $\rho_2$ and $h_2$ $(\rho_1 > \rho_2)$. The velocity of the liquid coming out of the hole is:

Medium

View Solution

$A$ tank is filled with water of density $1 \, g/cm^3$ and oil of density $0.9 \, g/cm^3$. The height of the water layer is $100 \, cm$ and the height of the oil layer is $400 \, cm$. If $g = 980 \, cm/s^2$,then the velocity of efflux from an opening in the bottom of the tank is

Difficult

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

Equal volumes of two immiscible liquids of densities $\rho$ and $2\rho$ are filled in a vessel as shown in the figure. Two small holes are punched at depths $h/2$ and $3h/2$ from the surface of the lighter liquid. If $v_1$ and $v_2$ are the velocities of efflux at these two holes,then $v_1/v_2$ is:

Similar Questions

$A$ wide vessel with a small hole at the bottom is filled with two liquids. The density and height of one liquid are $\rho_1$ and $h_1$ and that of the other are $\rho_2$ and $h_2$ $(\rho_1 > \rho_2)$. The velocity of the liquid coming out of the hole is:

$A$ tank is filled with water of density $1 \, g/cm^3$ and oil of density $0.9 \, g/cm^3$. The height of the water layer is $100 \, cm$ and the height of the oil layer is $400 \, cm$. If $g = 980 \, cm/s^2$,then the velocity of efflux from an opening in the bottom of the tank is

Vedclass Test Series

Exam Paper Generator

Online Exam Module