Arihant AIEEE Physics

D.B. Singh

Chapter 12

Some Mechanical Properties of Matter - all with Video Answers

Educators

Chapter Questions

Problem 1

The dimensions of Potsson's ratio is:
(a) $\left[\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}^{0}\right]$
(b) $\left[\mathrm{ML}^{-1} \mathrm{~T}^{-2}\right]$
(c) $\left[\mathrm{ML}^{2} \mathrm{~T}^{-4}\right]$
(d) $\left[\mathrm{ML}^{2} \mathrm{~T}^{-3}\right]$

Supratim Pal

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Problem 2

Une end of a wire 2 m long and diameter 2 mm, is fixed in a ceiling. A naughty boy of mass $10 \mathrm{~kg}$ jumps to catch the free end and slays there. The change in length of wire is : (lake $y=10 \mathrm{~m} / \mathrm{s}^{2}, Y=2 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}$ )
(a) $31.84 \times 10^{.5} \mathrm{~m}$
(b) 2 trum
(c) 3 inm
(d) 4111

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Problem 3

In above problem, if Poisson's ratio is $0=0.1$, the change in diameter is :
(a) $3.184 \times 10^{-5} \mathrm{~m}$
(b) $31.84 \times 10^{5} \mathrm{~m}$
(c) $3.184 \times 10^{8} \mathrm{~m}$
(d) $31.84 \times 10^{8} \mathrm{~m}$

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Problem 4

Two bodies of masses $1 \mathrm{~kg}$ and $2 \mathrm{~kg}$ are connected by a metal wire shown in figure. A force of $10 \mathrm{~N}$ is applied on the body of mass $2 \mathrm{~kg}$. The breaking stress of metal wire is $2 \times 10^{9} \mathrm{~N} / \mathrm{m}^{2}$.
What should be minimum radius of the wire used, if it is not to break?
(a) $0.23 \times 10^{-4} \mathrm{~m}$
(b) $4 \times 10^{-1} \mathrm{~m}$
(c) $5 \times 10^{-4} \mathrm{~m}$
(d) $5.2 \times 10^{-i} \mathrm{~m}$

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Problem 5

Two wires, one made of copper and other of steel are joined end to end. (as shown in figure). The area of cross-section of copper wire is twice that of steel wire.
They are placed under compressive force of magnitudes $F$. The ratio of their lengths such that change in lengths of both wires are same is: $\left(Y_{S}=2 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}\right.$ and $\left.Y_{C}=1.1 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}\right)$
(a) $2.1$
(b) $1.1$
(c) $1.2$
(d) 2

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Problem 6

The total elongation of the bar, if the bar is subjected to axial forces as shown in figure and the cross-sectional area of bar is $10 \mathrm{~cm}^{2}$, is : (Take $E=8 \times 10^{2} \mathrm{dyne} / \mathrm{cm}^{2}$ )
(a) $0.01 \mathrm{~cm}$
(b) $0.5 \mathrm{~cm}$
(c) $0.0675 \mathrm{~cm}$
(d) $0.775 \mathrm{~cm}$

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Problem 7

When tension in a metal wire is $T_{1}$, its length was $l_{1}$ and when tension is $T_{2}$, the length is $l_{2}$. Its unstretched length is:
(a) $\sqrt{l_{1} i_{2}}$
(b) $\frac{l_{1}+l_{2}}{2}$
(c) $\frac{\left(l_{1} T_{2}-l_{2} T_{1}\right)}{T_{2}-T_{1}}$
(d) $\frac{l_{1} T_{2}+T_{1} l_{2}}{T_{1}+T_{2}}$

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Problem 8

Three blocks system is shown in the figure. Each has mass $3 \mathrm{~kg}$. String connected to $P$ and $Q$ are of equal cross-section and Young's modulus of $0.005 \mathrm{~cm}^{2}$ and $2 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}$ respectively, neglect friction. The longitudinal strain in $A$ and $B$ are :
(a) $2.5 \times 10^{-4}, 1 \times 10^{-4}$
(b) $1 \times 10^{-4}, 2 \times 10^{-4}$
(c) $0.2 \times 10^{-4}, 2 \times 10^{-4}$
(d) none of these

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Problem 9

In the previous problem, the elastic potential energy stored per unit volume in wire connecting blocks $P$ in steady state is:
(Take $g=10 \mathrm{~m} / \mathrm{s}^{2}$ )
(a) $500 \mathrm{~J} / \mathrm{m}^{3}$
(b) $1000 \mathrm{~J} / \mathrm{m}^{3}$
(c) $2000 \mathrm{~J} / \mathrm{m}^{3}$
(d) $3000 \mathrm{~J} / \mathrm{m}^{3}$

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Problem 10

One end of a steel wire is fixed to ceiling of an elevator moving up with an acceleration $2 \mathrm{~m} / \mathrm{s}^{2}$ and a load of $10 \mathrm{~kg}$ hangs from other end. Area of cross-section of the wire is 2 $\mathrm{cm}^{2}$. The longitudinal strain in the wire is: (Take $g=10 \mathrm{~m} / \mathrm{s}^{2}$ and $\left.Y=2 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}\right)$
(a) $4 \times 10^{11}$
(b) $3 \times 10^{-6}$
(c) $8 \times 10^{-6}$
(d) $2 \times 10^{-6}$

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Problem 11

Equal weights are suspended from two wires of the same metal one of these wire is of length $2 \mathrm{~m}$ and diameter 1 $\mathrm{mm}$, while the other is of length $1 \mathrm{~m}$ and diameter $0.5$ $\mathrm{mm}$. Then :
(a) first wire has greater extension
(b) second wire has greater extension
(c) both wire have the same extension
(d) extension in both wires are zero

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Problem 12

Two wires one of copper and other of steel having same cross-sectional area and lengths $1.0 \mathrm{~m}$ and $0.5 \mathrm{~m}$ respectively, are fastened end to end and stretched by a load $M$. If copper wire is stretched by $1 \mathrm{~mm}$, the total extension of the combined wire is:
(Given: Young's modulii are $Y_{\text {copper }}=1 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}$, and $\left.Y_{\text {steel }}=2 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}\right)$
(a) $0.125 \mathrm{~cm}$
(b) $0.2 \mathrm{~cm}$
(c) $0.120 \mathrm{~cm}$
(d) $0.25 \mathrm{~cm}$

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Problem 13

Two bodies of masses $1 \mathrm{~kg}$ and $2 \mathrm{~kg}$ are connected by a steel wire of crosssection $2 \mathrm{~cm}^{2}$ going over a smooth pulley (as shown in figure). The longitudinal strain in the wire is:
(Take $g=10 \mathrm{~m} / \mathrm{s}^{2}$
$$
\left.Y=2 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}\right)
$$
(a) $3.3 \times 10^{-7}$
(b) $3.3 \times 10^{-6}$
(c) $2 \times 10^{-6}$
(d) $4 \times 10^{-6}$

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Problem 14

A body of mass $1 \mathrm{~kg}$ is fastened to one end of a steel wire of cross-sectional area $3 \times 10^{-6} \mathrm{~m}^{2}$ and is rotated in horizontal circle of radius $20 \mathrm{~cm}$ with a constant speed $2 \mathrm{~m} / \mathrm{s}$. The elongation of the wire is : $\left(Y=2 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}\right)$
(a) $0.33 \times 10^{-5} \mathrm{~m}$
(b) $0.67 \times 10^{-5} \mathrm{~m}$
(c) $2 \times 10^{-5} \mathrm{~m}$
(d) $4 \times 10^{-5} \mathrm{~m}$

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Problem 15

A body of mass $m=10 \mathrm{~kg}$ is attached to a wire of length $0.3 \mathrm{~m}$. The maximum angular velocity with which it can be rotated in a horizontal circle is: (Breaking stress of wire $=4.8 \times 10^{7} \mathrm{~N} / \mathrm{m}^{2}$ and area of cross-section of a wire $\left.=10^{-6} \mathrm{~m}^{2}\right)$
(a) $4 \mathrm{rad} / \mathrm{s}$
(b) $8 \mathrm{rad} / \mathrm{s}$
(c) $1 \mathrm{rad} / \mathrm{s}$
(d) $2 \mathrm{rad} / \mathrm{s}$

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Problem 16

Two equal parts of a cable are joined together. The maximum load that can be supported by either part is $w$. Then the maximum load that can be supported by the cable after joining is:
(a) $w / 2$
(b) $w / 3$
(c) $w / 4$
(d) $w$

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Problem 17

From the ceiling, a light rod of length $200 \mathrm{~cm}$ is suspended horizontally with the help of two vertical wires of equal length as shown in figure. If one wire is made of brass and have crosssectional area $0.2 \mathrm{~cm}^{2}$ and other of steel of $0.1 \mathrm{~cm}^{2}$ of cross-sectional area, then at what distance along rod a weight may be hung to produce equal stress in both the wires?
(a) $\frac{4}{3} \mathrm{~m}$ from steel wire
(b) $\frac{4}{3} \mathrm{~m}$ from brass wire
(c) $1 \mathrm{~m}$ from steel wire
(d) $\frac{1}{4} \mathrm{~m}$ from brass wire

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Problem 18

If a conical wire is stretched by two forces $F$ applied parallel to its length and in opposite direction, normal to end faces. The length of wire is $L$ and its end radius are $r_{1}$ and $r_{2}$. Find out the extension produced : (Given:
$Y=$ Young's modulus of wire)
(a) $\frac{F L}{\pi r_{1}^{2} Y}$
(b) $\frac{F L}{\pi r_{1} Y}$
(c) $\frac{F L}{\pi r_{1} r_{2} Y}$
(d) $\frac{F L Y}{\pi r_{1} r_{2}}$

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Problem 19

The velocity of projection of a missile of mass $5 \mathrm{~g}$, when a rubber cord is stretched to $12 \mathrm{~cm}$ and then released to project the missile, is: (Given: Area of cross-section of cord $=1 \mathrm{~mm}^{2}$, total unstretched length $=10 \mathrm{~cm}$, Young's modulus of rubber $=5 \times 10^{8} \mathrm{~N} / \mathrm{m}^{2}$ )
(a) $20 \mathrm{~m} / \mathrm{s}$
(b) $25 \mathrm{~m} / \mathrm{s}$
(c) $22 \mathrm{~m} / \mathrm{s}$
(d) $18 \mathrm{~m} / \mathrm{s}$

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Problem 20

When does an elastic metal rod change its length ?
(a) If it fall vertically under its weight
(b) If it is pulled along its length by a force acting at one end
(c) If it is rotated about an axis at one end
(d) If it slides on a smooth surface

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Problem 21

On what factor should the coefficient of restitution depend when two bodies having masses $m$ and $M$ $(m<M)$ collide with each other?
(a) Coefficient of restitution depends upon Young's modulus of elasticity of heavier body only
(b) Coefficient of restitution depends upon Young's modulus of elasticity of lighter body only
(c) Coefficient of restitution depends upon Young's modulus of elasticity of both the bodies
(d) Coefficient of restitution depends upon Nature of collision (wheather it is head on or oblique)

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Problem 22

If a metal wire of length $L$, having area of cross-section $A$ and Young's modulus $Y$, behaves as a spring of spring constant $k$. The value of $k$ is:
(a) $\frac{Y A}{L}$
(b) $\frac{Y A}{2 L}$
(c) $\frac{2 Y A}{L}$
(d) $\frac{Y L}{A}$

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Problem 23

Two identical springs of steel and copper are equally stretched. $W_{A}$ and $W_{B}$ represent works for steel and copper. Then:
(a) $W_{A}>W_{B}$
(b) $W_{A}<W_{B}$
(c) $W_{A}=W_{B}$
(d) $W_{A}>W_{B}$

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Problem 24

In the figure three identical springs are shown. From spring $A$, a mass of $4 \mathrm{~kg}$ is hung and spring shows elongation of $1 \mathrm{~cm}$. But when a weight of $6 \mathrm{~kg}$ is hung on $B$, the Hook's descends:
(a) $1 \mathrm{~cm}$
(b) $2 \mathrm{~cm}$
(c) $3 \mathrm{~cm}$
(d) $4 \mathrm{~cm}$

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Problem 25

A system consists of two springs and a mass $m=1 \mathrm{~kg}$ as shown in figure. If mass $m$ is displaced slightly along vertical and released. The system oscillates with a period of 2 sec. Then the spring constant $k$ is :
(a) $\frac{\pi^{2}}{4}$
(b) $\frac{\pi^{2}}{6}$
(c) $\frac{\pi^{2}}{8}$
(d) $\frac{\pi^{2}}{2}$

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Problem 26

Which of following graphs satisfies the Hooke's law under elastic limit?

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Problem 27

Elongation-load graph within elastic limit is shown in figure of three wires $A, B$ and $C$ made of same material and of same length. The thickest wire is:
(a) $A$
(b) $B$
(c) $C$
(d) none of the above

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Problem 28

What will happen if a metal wire is stretched a little beyond its elastic limit (or yield point) and released?
(a) It loses its elastic property completely
(b) It does not contract
(c) It contracts, but its final length will be greater than its initial length
(d) It contracts only up to its length at the elastic limit

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Problem 29

The linear strain in $x, y$ and $z$ -directions are $e_{x}, e_{y}$ and $e_{z}$ respectively. Then the volumetric strain is given by:
(a) $e_{x} e_{y} e_{z}$
(b) $e_{x}+e_{y}+e_{z}$
(c) $e_{t}=e_{x} e_{y}$
(d) $e_{z}=\frac{e_{r}+e_{y}}{2}$

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Problem 30

Young's modulus is defined for:
(a) solid
(b) liquid
(c) gas
(d) all of these

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Problem 31

The bulk modulus for an incompressible liquid is :
(a) $\infty$
(b) 0
(c) 1
(d) 2

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Problem 32

The value of modulus of rigidity for liquids is:
(a) $\infty$
(b) 0
(c) 1
(d) 2

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Problem 33

If for a material, $Y$ and $B$ are Young's modulus and Bulk modulus then :
(a) $Y<3 B$
(b) $Y=3 B$
(c) $Y>3 B$
(d) $3 Y=B$

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Numerade Educator

Problem 34

When a sphere is taken to bottom of sea $1 \mathrm{~km}$ deep, it contracts by $0.01 \%$. The bulk modulus of elasticity of the material of sphere is: (Given: Density of water $\left.=1 \mathrm{~g} / \mathrm{cm}^{3}\right)$
(a) $9.8 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$
(b) $10.2 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$
(c) $0.98 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$
(d) $8.4 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$

Narayan Hari

Numerade Educator

Problem 35

The stress for one litre of a perfect gas, at a pressure of $72 \mathrm{~cm}$ of $\mathrm{Hg}$, when it is compressed isothermally to a volume of $900 \mathrm{cc}$, is :
(a) $9.88 \times 10^{3} \mathrm{~N} / \mathrm{m}^{2}$
(b) $10.88 \times 10^{3} \mathrm{~N} / \mathrm{m}^{2}$
(c) $1.088 \times 10^{3} \mathrm{~N} / \mathrm{m}^{2}$
(d) $2 \times 10^{3} \mathrm{~N} / \mathrm{m}^{2}$

Narayan Hari

Numerade Educator

Problem 36

The force needed to punch a hole in shape of square of edge length $2 \mathrm{~cm}$ in a steel sheet $2 \mathrm{~mm}$ thick, is : (Given: Shearing stress $=3.5 \times 10^{8} \mathrm{~N} / \mathrm{m}^{2}$ )
(a) $5.6 \times 10^{3} \mathrm{~N}$
(b) $6.2 \times 10^{4} \mathrm{~N}$
(c) $5.6 \times 10^{4} \mathrm{~N}$
(d) $7.6 \times 10^{4} \mathrm{~N}$

Narayan Hari

Numerade Educator

Problem 37

If the shear modulus of a wire material is $5.9 \times 10^{11}$ dyne/cm $^{2}$ then the potential energy of a wire of $4 \times 10^{-3} \mathrm{~cm}$ in diameter and $5 \mathrm{~cm}$ long twisted through an angle of $10^{\prime}$, is :
(a) $1.253 \times 10^{-12} \mathrm{~J}$
(b) $2 \times 10^{-12} \mathrm{~J}$
(c) $1.00 \times 10^{-12} \mathrm{~J}$
(d) $0.8 \times 10^{-12} \mathrm{~J}$

Narayan Hari

Numerade Educator

Problem 38

Two cylinders of same material and of same length are joined end to end as shown in figure. The upper end of $A$ is rigidly fixed. Their radii are in ratio of $1: 2$ respectively. If the lower end of $B$ is twisted by an angle $\theta$, the angle of twist of cylinder $A$ is:
(a) $\frac{15}{16} \theta$
(b) $\frac{16}{15} \theta$
(c) $\frac{16}{17} \theta$
(d) $\frac{17}{16} \theta$

Narayan Hari

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Problem 39

What happen to the elastic property of a substance after annealing (cooling slowly after heating)?
(a) Increases
(b) Decreases
(c) Remain as such
(d) Becomes zero

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Problem 40

The curve in figure represents potential energy $(U)$ in between two atoms in a diatomic molecule as a function of distance ' $x^{\prime}$ between atoms. The atoms are :
(a) attracted when $x$ lies between ' $A^{\prime}$ and ' $B^{\prime}$ and repelled when $x$ lies between $B$ and $C$
(b) attracted when $x$ lies between $B$ and $C$ and repelled when $x$ lies between $A$ and $B$
(c) attracted when they reach $B$
(d) repelled when they reach $B$

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Problem 41

Surface tension of liquid:
(a) rises with rise in temperature
(b) fall with rise in temperature
(c) is independent of temperature
(d) none of the above

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Numerade Educator

Problem 42

A capillary tube of area of cross-section $A$ is dipped in water vertically. The amount of heat evolved as the water rises in the capillary tube up to height $h$ is : (The density of water is $\rho$ )
(a) $\frac{A p g h^{2}}{2}$
(b) $A g h^{2} \rho$
(c) $2 A g h^{\overline{2}} \rho$
(d) none of these

Narayan Hari

Numerade Educator

Problem 43

In an experiment a capillary tube is kept vertical, then water rises up in the tube up to $3 \mathrm{~mm}$ height. When the tube is tilted at an angle of $60^{\circ}$ with vertical, what should be the height of water rise?
(a) $6 \mathrm{~mm}$
(b) $4 \mathrm{~mm}$
(c) $3 \mathrm{~mm}$
(d) None of these

Narayan Hari

Numerade Educator

Problem 44

The rise of water in a capillary tube when kept vertical in water whose radii is $1 / 4$ th of that capillary tube which when kept, vertical water rise in it upto a height of $3 \mathrm{~mm}$, is:
(a) $12 \mathrm{~mm}$
(b) $10 \mathrm{~mm}$
(c) $4 \mathrm{~mm}$
(d) $3 \mathrm{~mm}$

Narayan Hari

Numerade Educator

Problem 45

The heat evolved for the rise of water when one end of the capillary tube of radius $r$ is immersed vertically into water, is: (Assume surface tension $=T$ and density of water to be $\rho$ )
(a) $\frac{2 \pi T}{\rho g}$
(b) $\frac{\pi T^{2}}{\rho g}$
(c) $\frac{2 \pi T^{2}}{\rho g}$
(d) none of these

Narayan Hari

Numerade Educator

Problem 46

Two parallel glass plates having separation ' $d^{\prime}$ are dipped in water. Some water rise up in the gap between the plates. The surface tension of water is $S$, atmospheric pressure $=P_{0}$, pressure of water just below the water surface in the region between the plates is $P$, find the relation between them :
(a) $P=P_{0}-\frac{2 S}{d}$
(b) $P=P_{0}+\frac{2 S}{d}$
(c) $P=P_{0}-\frac{4 S}{d}$
(d) $P=P_{0}+\frac{4 S}{d}$

Narayan Hari

Numerade Educator

Problem 47

In a liquid there is air bubble of radius $1 \mathrm{~mm}$ at a depth $10 \mathrm{~cm}$ below the free space. The surface tension of liquid is $0.075 \mathrm{~N} / \mathrm{m}$ and density is $1000 \mathrm{~kg} / \mathrm{m}^{3}$. By what amount is the pressure inside the bubble greater than the atmospheric pressure?
(a) 1130 pascal
(b) 1200 pascal
(c) 1100 pascal
(d) 1000 pascal

Narayan Hari

Numerade Educator

Problem 48

The work done by a boy in making a soap bubble of diameter $1.4 \mathrm{~cm}$ by blowing, if the surface tension of soap solution is $0.03 \mathrm{~N} / \mathrm{m}$, is :
(a) $3 \times 10^{-5} \mathrm{~J}$
(b) $3.696 \times 10^{-5} \mathrm{~J}$
(c) $2 \times 10^{-5} \mathrm{~J}$
(d) $4.2 \times 10^{-5} \mathrm{~J}$

Narayan Hari

Numerade Educator

Problem 49

A drop of radius $r$ is broken into $n$ equal drops. The work done if surface tension of water is $T$, is:
(a) $4 r \pi R^{2} n T$
(b) $4 \pi R^{2} T\left(n^{2 / 3}-1\right)$
(c) $4 \pi R^{2} T\left(n^{1 / 3}-1\right)$
(d) none of these

Narayan Hari

Numerade Educator

Problem 50

What will happen if $n$ drops of a liquid each has surface energy $E$, combine to form a single drop?
(a) No energy will be released in the process
(b) Some energy will be absorbed in the process
(c) Energy released or absorbed will be $E\left(n-n^{2 / 3}\right)$
(d) Energy released or absorbed will be $n E\left(2^{2 / 3}-1\right)$

Narayan Hari

Numerade Educator

Problem 51

If a bigger drop of liquid at temperature $t$, breaks up into number of small droplets, then what is temperature of the droplets? (Assume bigger drop is isolated from its surroundings)
(a) Equal to $t$
(b) Greater than $t$
(c) Less than $t$
(d) Either (a), (b), (c) depending on surface tension of liquid

Narayan Hari

Numerade Educator

Problem 52

The excess pressure inside a soap bubble of radius $4 \mathrm{~cm}$ is 30 dyne $/ \mathrm{cm}^{2}$. The surface tension is :
(a) 30 dyne $/ \mathrm{cm}$
(b) 20 dyne $/ \mathrm{cm}$
(c) 40 dyne $/ \mathrm{cm}$
(d) 80 dyne $/ \mathrm{cm}$

Narayan Hari

Numerade Educator

Problem 53

The work done against surface tension in formation of a drop of mercury of radius $4 \mathrm{~cm}$ is :
(surface tension for mercury $=465$ dyne $/ \mathrm{cm}$ )
(a) $9.34 \times 10^{-3} \mathrm{~J}$
(b) $10 \times 10^{-2} \mathrm{~J}$
(c) $4 \times 10^{-3} \mathrm{~J}$
(d) $466 \mathrm{~J}$

Narayan Hari

Numerade Educator

Problem 54

The energy required to increase the radius of a soap bubble from $1 \mathrm{~cm}$ to $2 \mathrm{~cm}$ is: (The surface tension is 30 dyne $/ \mathrm{cm}$ )
(a) $240 \pi \mathrm{erg}$
(b) $720 \pi$ erg
(c) $480 \pi$ erg
(d) none of these

Narayan Hari

Numerade Educator

Problem 55

A film of a liquid is held on a circular ring of radius $r$. If the surface tension of the liquid is $T$, the surface energy of liquid is :
(a) $\pi r^{2} T$
(b) $2 \pi r^{2} T$
(c) $4 \pi r^{2} T$
(d) none of these

Narayan Hari

Numerade Educator

Problem 56

The common radius of curvature ' $r^{\prime}$, when two soap bubbles with radii $r_{1}$ and $r_{2}\left(r_{1}>r_{2}\right)$ come in contact, is:
(a) $r=\frac{r_{1}+r_{2}}{2}$
(b) $r=\frac{r_{1} r_{2}}{r_{1}-r_{2}}$
(c) $r=\frac{r_{1} r_{2}}{r_{1}+r_{2}}$
(d) $r=\sqrt{r_{1} r_{2}}$

Narayan Hari

Numerade Educator

Problem 57

Water is flowing in a river. If the velocity of a layer at a distance $10 \mathrm{~cm}$ from the bottom is $20 \mathrm{~cm} / \mathrm{s}$, the velocity of layer at a height of $40 \mathrm{~cm}$ from the bottom is:
(a) $10 \mathrm{~m} / \mathrm{s}$
(b) $20 \mathrm{~cm} / \mathrm{s}$
(c) $30 \mathrm{~cm} / \mathrm{s}$
(d) $80 \mathrm{~cm} / \mathrm{s}$

Narayan Hari

Numerade Educator

Problem 58

A horizontal plate $(10 \mathrm{~cm} \times 10 \mathrm{~cm})$ moves on a layer of oil of thickness $4 \mathrm{~mm}$ with constant speed of $10 \mathrm{~cm} / \mathrm{s}$. The coefficient of viscosity of oil is 4 poise. The tangential force applied on the plate to maintain the constant speed of the plate is :
(a) $10^{3}$ dyne
(b) $10^{4}$ dyne
(c) $10^{5}$ dyne
(d) none of these

Narayan Hari

Numerade Educator

Problem 59

A liquid is flowing through a narrow tube. The coefficient of viscosity of liquid is $0.1308$ poise. The length and inner radius of tube are $50 \mathrm{~cm}$ and $1 \mathrm{~mm}$ respectively. The rate of flow of liquid is $360 \mathrm{~cm}^{3} / \mathrm{min}$. The pressure difference between ends of tube is:
(a) $10^{6}$ dyne $/ \mathrm{cm}^{2}$
(b) $10^{4}$ dyne $/ \mathrm{cm}^{2}$
(c) $10 \mathrm{dyne} / \mathrm{cm}^{2}$
(d) none of these

Narayan Hari

Numerade Educator

Problem 60

The terminal velocity of solid sphere of radius $0.1 \mathrm{~m}$ moving in air in vertically downward direction, is:
(\eta $=1.8 \times 10^{-5} \mathrm{Ns} / \mathrm{m}^{2}$, density of sphere $=1000 \mathrm{~kg} / \mathrm{m}^{3}$ and
$\left.g=10 \mathrm{~m} / \mathrm{s}^{2}\right)$
(a) $2 \times 10^{5} \mathrm{~m} / \mathrm{s}$
(b) $1.2 \times 10^{8} \mathrm{~cm} / \mathrm{s}$
(c) $4 \times 10^{2} \mathrm{~cm} / \mathrm{s}$
(d) none of these

Narayan Hari

Numerade Educator

Problem 61

Eight equal drops of water each of radius $r=2 \mathrm{~mm}$ are falling through air with a terminal velocity of $16 \mathrm{~cm} / \mathrm{s}$. The eight drops combine to form a big drop. The terminal velocity of big drop is:
(a) $16 \mathrm{~cm} / \mathrm{s}$
(b) $32 \mathrm{~cm} / \mathrm{s}$
(c) $64 \mathrm{~cm} / \mathrm{s}$
(d) none of these

Narayan Hari

Numerade Educator

Problem 62

At $20^{\circ} \mathrm{C}$, to attain the terminal velocity how fast will an aluminium sphere of radii $1 \mathrm{~mm}$ fall through water? [Assume flow to be laminar flow and specific gravity $\left.(\mathrm{Al})=2.7, \eta_{\text {water }}=8 \times 10^{-4} \mathrm{~Pa}\right]$
(a) $5 \mathrm{~m} / \mathrm{s}$
(b) $4.7 \mathrm{~m} / \mathrm{s}$
(c) $4 \mathrm{~m} / \mathrm{s}$
(d) $2 \mathrm{~m} / \mathrm{s}$

Narayan Hari

Numerade Educator

Problem 63

The journey of a small spherical solid ball dropped in a viscous liquid is best described by:
(a) curve $A$
(b) curve $B$
(c) curve $C$
(d) curve $D$

Narayan Hari

Numerade Educator

Problem 64

The speed of flow of water through a long cylindrical pipe of diameter $2 \mathrm{~cm}$ so that flow become turbulent, is:
(Assume at temperature of $20^{\circ} \mathrm{C}$, viscosity $\eta=1 \times 10^{-3} \mathrm{~Pa} .$ second, Reynold number $=3000$ )
(a) $1.5 \mathrm{~m} / \mathrm{s}$
(b) $0.15 \mathrm{~m} / \mathrm{s}$
(c) $2 \mathrm{~m} / \mathrm{s}$
(d) $1 \mathrm{~m} / \mathrm{s}$

Narayan Hari

Numerade Educator