New chat PYQ Library Doubts Rank report

Sign in to see Recents

Your guest activity stays on this device

Sign in to save progress →

Properties of Matter question

2020 · 7 Jan · Shift 2 · Q52

Guest · filters and generic practice availableBrowsing as a guest · PYQ filters and generic practice are available. Sign in only for personalised features and saved progress.

PYQ Library
JEE Main
Physics
Properties of Matter
2020 · 7 Jan · Shift 2 · Q52

Properties of Matter question

2020 · 7 Jan · Shift 2 · Q52

JEE MainPhysicsProperties of MatterMCQ+4 / −1

An ideal fluid flows (laminar flow) through a pipe of non-uniform diameter. The maximum and minimum diameters of the pipes are 6.4 cm and 4.8 cm, respectively. The ratio of the minimum and the maximum velocities of fluid in this pipe is :

A
${3 \over 4}$
B
${9 \over {16}}$
C
${{\sqrt 3 } \over 2}$
D
${{81} \over {256}}$

View written solutionFree

Correct answer: B

Use equation of continuity for an ideal incompressible fluid:

$A v = \text{constant}$

So, velocity is inversely proportional to cross-sectional area:

$v \propto \frac{1}{A}$

Since the pipe is circular,

$A = \frac{\pi d^2}{4}$

Thus,

$v \propto \frac{1}{d^2}$

Identify where maximum and minimum velocities occur:

Maximum velocity occurs at minimum diameter $d_{\min} = 4.8\,\text{cm}$
Minimum velocity occurs at maximum diameter $d_{\max} = 6.4\,\text{cm}$

Find the required ratio:

We need

$\frac{v_{\min}}{v_{\max}} = \frac{1/d_{\max}^2}{1/d_{\min}^2} = \frac{d_{\min}^2}{d_{\max}^2}$

Substitute values:

$\frac{v_{\min}}{v_{\max}} = \left(\frac{4.8}{6.4}\right)^2$

$= \left(\frac{48}{64}\right)^2 = \left(\frac{3}{4}\right)^2$

$= \frac{9}{16}$

Check options:

A: $\frac{3}{4}$
B: $\frac{9}{16}$
C: $\frac{\sqrt{3}}{2}$
D: $\frac{81}{256}$

Hence, the correct option is B.

More from Properties of Matter

Consider a solid sphere of radius R and mass density $ρ (r) = ρ_{0} (1 - \frac{r ^{2}}{R ^{2}})$ , $0 < r \leq R$ The minimum density of a liquid in which it will float is :2020 · MCQ
A leak proof cylinder of length 1m, made of a metal which has very low coefficient of expansion is floating vertically in water at 0°C such that its height above the water surface is 20 cm. When the temperature of water is increased to…2020 · MCQ
Two liquids of densities $ρ_{1}$ an $ρ_{2}$ ( $ρ_{2}$ = 2 $ρ_{1}$ ) are filled up behind a square wall of side 10 m as shown in figure. Each liquid has a height of 5 m. The ratio of the forces due to these liquids exerted on… Includes diagram2020 · MCQ
Water flows in a horizontal tube (see figure). The pressure of water changes by 700 Nm–2 between A and B where the area of cross section are 40 cm2 and 20 cm2, respectively. Find the rate of flow of water through the tube. (density of… Includes diagram2020 · MCQ
Two steel wires having same length are suspended from a ceiling under the same load. If the ratio of their energy stored per unit volume is 1 : 4, the ratio of their diameters is:2020 · MCQ
A small spherical droplet of density d is floating exactly half immersed in a liquid of density $ρ$ and surface tension T. The radius of the droplet is (take note that the surface tension applies an upward force on the droplet) :2020 · MCQ
A steel wire having a radius of 2.0 mm, carrying a load of 4 kg, is hanging from a ceiling. Given that g = 3.1 p ms–2, what will be the tensile stress that would be developed in the wire ?2019 · MCQ
Water from a pipe is coming at a rate of 100 litres per minute. If the radius of the pipe is 5 cm, the Reynolds number for the flow is of the order of : (density of water = 1000 kg/m3, coefficient of viscosity of water = 1mPas)2019 · MCQ