# WBBSE Class 9 Physical Science Solutions Chapter 3 Matter: Structure and Properties

Detailed explanations in West Bengal Board Class 9 Physical Science Book Solutions Chapter 3 Matter: Structure and Properties offer valuable context and analysis.

## WBBSE Class 9 Physical Science Chapter 3 Question Answer – Matter: Structure and Properties

Question 1.
What is the unit of density in SI System ?
The unit of density in SI system is : kgm-3.

Question 2.
What is the unit of specific gravity in CGS system ?
The unit of specific gravity in CGS system is : gcm-3.

Question 3.
What is fluid?
The word fluid cames from a Latin word ‘fluere’ meaning ‘to flow’.

Question 4.
Is pressure a scalar quantity ?
No, pressure is not a scalar quantity. It is a vector quantity.

Question 5.
Give the dimensional formula of pressure.
The dimensional formula of pressure is : [ML-1 T-2].

Question 6.
What is the relation between density and specific gravity of substance?
Density of a substance = specific gravity of the substance × density of water at 4°.

Question 7.
What is buoyancy?
The upward thrust which any fluid exerts upon a body partly or wholly submerged in it is called its buoyancy.

Question 8.
Does buoyancy depend on the depth of the liquid to which a body is immersed?
The buoyancy does not depend on the depth of the liquid to which the body is immersed.

Question 9.
Is there any gas in the Torricellian space?
The empty space above the mercury level in the tube contains practically nothing but a negligible amount of mercury vapour and is known as Torricellian space.

Question 10.
Will the siphon work, if there be a hole at any point in the longer arm above the surface of the liquid in the vessel in which the shorter arm is placed?
When a hole is made at any point in the longer arm above the surface of the liquid in the vessel in which the shorter arm is placed, siphon will not work.

Question 11.
Is surface tension a vector quantity ?
Surface tension is a scalar quantity as it has no specific direction.

Question 12.
What is the unit of surface energy ?
The unit of surface energy is Joule.

Question 13.
What is capillarity ?
The phenomenon of rise or fall of liquid in a capillary tube is called capillarity.

Question 14.
Define ‘angle of contact’.
The angle which the tangent to the liquid surface at the point of contact makes with the solid surface inside the liquid is called angle of contact.

Question 15.
What happens to surface tension, when impurity is mixed in it ?
The presence of impurities in the liquid surface or dissolved in it, considerably affect force of surface tension and depends on the degree of contamination.

Question 16.
How rough sea can be calmed ?
Rough sea can be calmed by pouring oil on sea water.

Question 17.
In a streamline flow, what is the velocity of the liquid in contact with the containing vessel.
Zero.

Question 18.
What is terminal velocity ?
Terminal velocity of a body is the constant maximum velocity acquired by a body while falling through a viscous fluid.

Question 19.
Can two streamline cross each other ?
No.

Question 20.
What is the terminal velocity of a body in a freely falling system?
Terminal velocity of a body in a freely falling system is zero.

Question 21.
What is the acceleration of a body falling through a viscous fluid after terminal velocity is reached?
Zero.

Question 22.
Velocity of water in a river is less on the bank and large in the middle. Explain.
Velocity of water in contact with solid banks is zero and it increases as we go towards the middle of the river.

Question 23.
The velocity of fall of a man jumping with a parachute first increases and then become constant. Why?
It is because of the fact the man attains terminal velocity.

Question 24.
What is the SI unit of coefficient of viscosity ?
The SI unit of coefficient of viscosity is Decapoise (Nsm-2).

Question 25.
What is critical velocity ?
Critical velocity : It is the velocity of flow of a liquid upto which its flow is streamlined and above which its flow becomes turbulent.

Question 26.
Does viscosity come into play if there is relative motion of the liquid layers?
Yes, it depends on the relative velocity of two layers.

Question 27.
Does viscosity depend on the area of the layers in contact ?
Viscosity depends on the area of the liquid layers.

Question 28.
What do you mean by an ideal fluid?
An ideal fluid has zero viscosity and zero compressibility.

Question 29.
Is viscosity a vector quantity ?
No, viscosity is a scalar quantity.

Question 30.
Write down the dimensional formula for coefficient of viscosity.
The dimensional formula for coefficient of viscosity is : [ML-1T-1].

Question 31.
How does the viscosity of a liquid change with the change in temperature?
The viscosity of a liquid increases with decrease in temperature and vice-versa.

Question 32.
How does the viscosity of a gas change with the change in temperature?
The viscosity of a gas increases with increase in temperature and vice-versa.

Question 33.
What is the value of Reynolds number for streamline flow ?
NR < 2000.

Question 34.
Why does air bubble in a liquid rise up ?
As terminal velocity of an air bubble is negative.

Question 35.
Is Bernoulli’s theorem valid for viscous liquid?
No.

Question 36.
Water and castor oil taken in two different flasks and shaken violently and kept on a table. Which liquid will come to rest earlier?
Castor oil having higher viscosity will come to rest earlier.

Question 37.
Out of friction force and viscous force, which one depends on velocity?
Viscous force depends on velocity, but friction force is independent of velocity.

Question 38.
The hotter liquid flows faster than colder one. Why ?
The coefficient of viscosity of liquid decreases with rise in temperature and so liquid flows faster.

Question 39.
What are the properties of a liquid satisfying Bernoulli’s theorem ?
The liquid must be ideal one.

Question 40.
What are the dimensions of stress and strain ?
Stress = [ML-1T-2] and strain = [M°L°T°]

Question 41.
What is more elastic – water or air ?
Water Bulk modulus of elasticity is reciprocal of compressibility and air is more compressible than water.

Question 42.
Why are springs made of steel and not of copper?
Modulus of elasticity of steel is more than that of copper.

Question 43.
What is the value of modulus of rigidity for a liquid ?
Zero

Question 44.
What is the value of young’s modulus for an incompressible liquid?
Zero

Question 45.
What is the unit of Poisson’s ratio?
No unit

Question 46.
What is the value of bulk modulus for an incompressible liquid ?
Infinite

Question 47.
What is more elastic – steel or rubber ?
Steel

Question 48.
What is more fundamental – stress or strain ?
Strain is more fundamental, as stress is developed only when a body is strained.

Question 49.
Is poisson’s ratio an elastic modulus ?
No. Poisson’s ratio is unitless while elastic modulus has unit Nm-2.

Question 50.
Is there any truly rigid body ?
No, there is to truly rigid body.

Question 51.
What is hydrostatic pressure?
Hydrostatic pressure : The normal force exerted by the fluid at rest per unit area of the surface in contact with it is called the pressure of fluid or hydrostatic pressure.

Question 52.
What is S.I. unit of pressure?
The S.I. unit of pressure is Nm-2 or pascal (Pa}).

Question 53.
Define thrust.
Thrust – The total normal force exerted by a fluid at rest on a surface in contact with it, is thrust.

Question 54.
What is the unit of thrust in S.I. ?
The unit of thrust is newton (N).

Question 55.
State the relationship between thrust and pressure.
Thrust = Pressure × Area.

Question 56.
When an object is immersed in a fluid, name the two forces acting on it.
Two forces are upward thrust and weight of the body.

Question 57.
Define upthrust.
When a body is immersed partly or fully in a fluid, it appears to become lighter. This occurs due to the fact that the fluid exerts an upthrust on the immersed object.

Question 58.
State Archimedes’ principle.
Archimedes’ principle : It states that a body immersed wholly or partly in a fluid at rest, appears to lose a part of its weight, which is equal to the weight of the fluid displaced.

Question 59.
Define relative density.
Relative density : Relative density of a substance is the ratio of the density of the substance to the density of pure water at 4°.

Question 60.
Define density. Give S.I. unit of density.
Density : Density of a substance is its mass per unit volume.
S.I. unit of density : Kgm-3

Question 61.
What is meant by atmosphere?
Atmosphere : The earth’s surface is surrounded by air extending upto a height of about 500 km which is called atmosphere.

Question 62.
Name the instrument used for measuring atmospheric pressure.
Barrometer is an instrument for measuring the pressure of the atmosphere.

Question 63.
What is the value of normal atmospheric pressure?
Normal atmospheric pressure is the pressure exerted by the 760 mm length of mercury column.

Question 64.
What is siphon ?
Siphon : Siphon is a simple device for transferring liquid from one vessel to the other without disturbing the whole volume of the liquid.

Question 65.
What is the unit of surface tension in SI ?
Nm-1 is the unit of surface tension in SI.

Question 66.
State whether surface tension is a scalar or vector quantity.
Surface tension is a scalar quantity as it has no specific direction.

Question 67.
What is streamlines ?
Streamlines : In streamline flow, the path of any particle of the fluid is always directed along the line of motion of the fluid and each particle in the fluid travels in exactly the same path, which is called a streamline, as the particle preceding it.

Question 68.
On what princple is Bernoulli’s theorem based?
Bernoulli’s theorem is based on the principle of conservation of energy applied to a liquid in motion.

Question 69.
What is stress ?
stress : Whenever a deforming force is applied to a body, an internal reaction force is developed in it which tends to resist the applied force and also to maintain the original shape and size of the body. The restoring force developed per unit area of the body is called stress.

Question 70.
Define strain. what is its unit?
Strain : It is the ratio of the change in length, volume or shape to the original configuration.
The strain being the ratio of two similar quantities is a pure number having no unit.

Question 71.
What is the SI unit of stress ?
SI unit of stress is dyne/cm2.

Question 72.
State Hooke’s law.
Hooke’s law : Within elastic limit, the stress developed in a body is proportional to the strain produced in it.

Question 73.
Mention one use of elasticity in our deaily life.
The metallic parts of machineries are so designed that they are not subject to possible stress beyond elastic limit.

Question 1.
A floating body loses its weight – explain.
Explanation : The weight of a floating body is equal to the weight of the liquid displaced by it. These two forces act in opposite direction along the vertical line. Thus these forces balance each other and apparently floating body loses weight.

Question 2.
Does siphon work on the surface of moon ? Explain.
Explanation: There being no atmosphere in the moon, there is no atmospheric pressure. So, siphon does not work on the moon.

Question 3.
Explain whether the rate of flow of liquid through a siphon will change if the atmospheric pressure changes.
Explanation : No. The rate of flow of liquid through a siphon depends on the differences of pressures of liquid columns in its two limbs and not on the barometric pressure.

Question 4.
Can you siphon out water from a leaking boat to the river ?
Explanation : No, the boat is floating on the river and water leaks into the boat from the river. Thus water inside the boat would be always in the same level as that of the river outside. So it is not possible to siphon out water in this case.

Question 5.
Why should a field be ploughed before sowing?
Explanation: This is done to break the tiny capillaries through which water rises and finally evaporates. The ploughing of field helps the soil to retain the moisture.

Question 6.
Explain why oil rises in the wick of a lamp?
Explanation : The pores in the wick serve the purpose of a number of line capillaries. The oil rises due to capillary action.

Question 7.
Will the rate of flow change in a siphon if water be replaced by mercury ?
No, the rate of flow of liquid in a siphon does not depend on the density of the liquid.

Question 8.
Can you use water in a barometer?
The height of water barometer would be about 10 ~m}, which is not practicable.Further water sticks to glass and water is to be coloured.

Question 9.
Why water does not wet a glass rod coated with wax ?
Because, force of adhesion between water and wax is less than the force of cohesion between water molecules.

Question 10.
Why mercury does not wet glass ?
The cohesive force between mercury molecules is greater than the adhesive force between mercury and glass.

Question 11.
Why hot soup tastes better than cold soup?
The surface tension of hot soup is less than the cold soup and thus soup spreads over larger area of the tongue.

Question 12.
Why soap bubble burst after sometime?
Soap bubbles burst when pressure inside them become more than outside atmospheric pressure. So, soap bubbles burst after sometime.

Question 13.
The diameter of a ball is twice that of another ball. What will be the ratio of the their terminal velocities in water ?
We know that, the terminal velocity is directly proportional to the square of the radius of the ball. i.e.
The terminal velocity α (radius of the ball)2
∴ ratio of their terminal velocities will be 4 : 1

Question 14.
Water is coming out of a hole made on the wall of a fresh water tank. If the size of the hole is increased, (i) will the velocity of efflux of water change? (ii) Will the volume of water coming out per second change?
(i) Velocity of efflux remains unaltered, as it depends only on the depths of the hole below the fresh surface of water.
(ii) Volume changes, as volume of the liquid flowing per second depends upon the area of cross-section of the hole.

Question 15.
Explain, why still water runs deep?
Explanation : From equation of continuity, we have, a v= constant.
The speed of still water is very small and so area would be large. Thus still water becomes deep.

Question 16.
Why does the velocity increase, when water flowing in a broader pipe enters into a narrower pipe?
From equation of continuity, we have a v = constant. So, when water enters into a narrower pipe flowing from a broader pipe, then area of cross-section decreases and thus velocity of flow increases.

Question 17.
Small air bubbles rise slower than the bigger one through a liquid, why?
The terminal velocity of a bubble is proportional to the square of the radius of the bubble. So, smaller air bubbles having smaller radii would have low values of terminal velocities and rise with slower rate.

Question 18.
Why do clouds float in the sky?
The tiny drops of water present in clouds have negligibly small terminal velocity. So, clouds float in the sky.

Question 19.
Why should the lubricant oils be of high viscosity ?
Lubricants are used for decreasing dry friction between different parts of the machines. The lubricants with high viscosity would stick to the machine parts and would not come out during movements of the machine parts.

Question 20.
Why is viscosity called internal friction?
There is a backward drag on each of the upper layer of a flowing liquid by the lower layer. So, viscosity acts like friction from within and thus it is called internal friction.

Question 21.
What is elasticity ?
Elasticity : It is the property by which a body is able to resist deformation, either in shape or in volume or both, and recovers its original configuration when the deforming force is removed.

Question 22.
What is elastic limit ?
Elastic limit : It is the upper limit of deforming force upto which the body regains its original shape or size completely or removal of deforming force and beyond which on increasing the deforming force, the body loses its property of elasticity and gets permanently deformed.

Question 23.
‘The poisson’s ratio depends only on the nature of the material and not at all on the stress applied within elastic timit’ – explain.
Poisson’s ratio = $$\frac{\text { lateral strain }}{\text { longitudinal strain }}$$
which does not involve stress within elastic limit and depends only on the nature of the material.

Question 24.
What is Hooke’s law ? What is generalised Hook’s law ?
bullet Hooke’s law : The deformation of an elastic body is directly proportional to the applied force within elastic limit.
Generalised Hooke’s law : Within elastic limit, stress is proportional to strain.

Question 25.
What is elastic fatigue?
The property of an elastic body by virtue of which its behaviour becomes less elastic under the action of repeated alternating deforming forces is called elastic fatigue.

Question 26.
What is Tensile stress ?
Tensile stress : If there be increase in length or extension of a body in the direction of the applied force, the stress developed is called tensile stress.

Question 1.
How will the reading of a mercury barometer, placed inside a lift, change if the lift starts moving downwards with a given acceleration? Give reasons for your answer.
Reason : Let the lift descend with acceleration f. Then effective acceleration with which it descends will be (g-f). Thus the weight of mercury column in the barometer decreases. But atmospheric pressure remaining the same, the height of the mercury column in the barometer would be more.

Question 2.
Why are small liquid drops spherical in shape, while big drops are flat ?
A liquid drop attains spherical shape to have minimum surface area and hence minimum potential energy state. In a small liquid drop the force due to surface tension is large compared to the force due to weight of the drop or gravitational pull and the drop attains spherical shape. But as the size of the drop increases, its weight also increases, which pulls the drop downwards and it becomes flat.

Question 3.
Water rise in a capillary tube whereas mercury falls in the same tube. Explain.
Explanation: The cohesive force between mercury molecules is much larger than the force of adhesion between mercury and glass. While the force of adhesion between water and glass is much more than the force of cohesion between water molecules.

Question 4.
Two soap bubbles of unequal sizes are blown at the ends of a capillary tube. Which one will grow at the cost of the other?
Excess of pressure p is inversely proportional to the radius r of the soap bubble i.e. p inside a small bubble will be more than that inside the large bubble. So, big bubble will grow at the cost of smaller one.

Question 5.
Oil spreads over the surface of water while does not do so on oil surface. Explain.
Explanation : Surface tension of oil is less than the surface tension of water. So on spreading oil on the surface of water, it spreads in all directions due to the higher force of surface tension of water.

Question 6.
Why does surface tension vary with temperature?
With the increase of temperature, the force of cohesion of the liquid molecules decreases. So surface tension decreases with increase of temperature.

Question 7.
Why do two mercury drops form one drop when brought in contact?
Explanation : Liquids tend to attain minimum surface area state due to surface tension. When two drops come in contact, they form a single drop for decreasing surface area.

Question 8.
Explain how a spider walks easily on the surface of water.
Explanation: The free surface of water behaves as a stretched membrane due to surface tension. This membrane is depressed due to the weight of the spider. The vertical component of the surface tension balances the weight of the spider and hence it is able to walk on the water surface.

Question 9.
A needle may float on clean water but sinks in water having detergent. explain.
Explanation : The free surface of water acts like a stretched membrane due to surface tension and a needle can float on it. But on adding some detergent, surface tension of water decreases and the tension in the membrane is weakened and it can no longer hold the weight of the needle.

Question 10.
Small pieces of camphor dance when placed on the surface of water. Why ?
Surface tension of water decreases when camphor dissolves in it. Due to its irregular shape, the camphor dissolves unevenly on different sides. So, unbalanced surface tension forces act on the camphor and hence the piece of camphor moves randomly in different directions.

Question 11.
The velocity of water in a river is less on the bank and large in the middle; why?
Explanation: The water in the river flows in the form of streams. The forces of adhesion is less on the streams in the middle of the river than near the bank. So, the velocity of streams near the bank is minimum and is maximum in the middle of the river.

Question 12.
Explain the effect of (i) density (ii) temperature (iii) pressure on the viscosity of liquids and gases.

1. With increase in density, viscosity of liquid increases, while for gases, it decreases.
2. With increase in temperature, viscosity of liquid decreases, while that of gases increases.
3. With increase in pressure, the viscosity of liquids except water increases and that of water decreases. In the case of gases viscosity is practically independent of pressure.

Question 13.
How will the weight of a body be affected, when it falls with its terminal velocity through a viscous medium?
When a body falls through a viscous medium with its terminal velocity, it moves with constant velocity. So, no resultant force is acting on the body, as pull due to gravity is balanced by viscous drag and buoyancy of medium. Hence the effective weight of the body becomes zero.

Question 14.
The stream of water flowing at high speed from a garden hose pipe tends to spread like a fountain when held vertically up, but tends to narrow down when held vertically down. Why?
As the stream falls, its speed v increases and consequently its area of cross-section, a will decrease, according to equation of continuity,
av = constant, and hence the stream becomes narrow.
When the stream goes up, its speed decreases, so, its area of crosssection increases and hence it becomes broader and spreads out like a fountain.

Question 15.
It is advised not to stand near a running train. Why ?
When a fast moving train passes on a rail, the velocity of streams of air between the rail and the man standing near the rail will be larger than the velocity of air streams on the other side of the man away from the rail. Following Bernoulli’s theorem, the pressure of air will be low in between the man and the rail and high on the other side of the man. Thus the man may be pushed towards the rail and may meet with an accident.

Question 16.
Define stress and strain. Give their units.
Stress : Whenever a deforming force is applied to a body, internal force of reaction comes into play, which tends to resist the deforming force and maintains the original configuration of the body. This reaction force developed per unit area of the body is called stress.
Units of stress : (i) CGS unit : dyne cm-2 (ii) SI unit : Nm-2
Strain : When a deforming force is applied on a body, there is a change in the configuration of the body and the body is said to be strained i.e., the strain is the measure of the amount of deforming produced in the body.
unit of strain : (i) CGS : No unit (ii) SI : No unit [Strain being the ratio of two like quantities has no unit ]

Question 17.
Define longitudinal stress. What is its unit in (i) CGS system (ii) SI system ?
Longitudinal Stress : If there be increase in length or extension of a body in the direction of the applied force, the stress developed is called longitudinal stress.
Unit of longitudinal stress : (i) CGS : dyne cm-2 (ii) SI : Nm-2

Question 18.
State and Explain Hooke’s law.
Hooke’s Law : The deformation of an elastic body is directly proportional to the applied force within elastic limit.
Afterfwards English scientist Thomas Young modified the law to a general form and is known as generalised Hooke’s law.
This is stated as :
Within elastic limit, stress is proportional to strain. Thus, within elastic limit, stress α strain
$$\text { or, } \frac{\text { stress }}{\text { strain }}=\text { constant }$$
This proportionality constant is known as coefficient of elasticity or modulus of elasticity of a body which is independent of magnitude of stress and strain but depends upon the nature of the material of the body and the way in which the body is deformed.

Question 19.
Define : (i) young’s modulus (ii) Bulk modulus (iii) Modulus of rigidity (iv) Poisson’s ratio.
(i) Young’s modulus : Young’s modulus of elasticity is the ratio of the longitudinal stress to the longitudinal strain within the elastic limit.
(ii) Bulk modulus : Bulk modulus of elasticity is the volume stress (normal stress) to the volume strain within elastic limit.
(iii) Modulus of rigidity : Modulus of rigidity or shear modulus of a material is the ratio of the shearing stress to the shearing strain within elastic limit.
(iv) Poisson’s ratio : The ratio of the lateral strain to longitudinal strain of the material of a wire or bar under tension is called its poisson’s ratio.

Numerical Problems

Working formula :

(i) D = $$\frac{m}{v}$$ (D = density, m = mass, v = volume)
(ii) P = $$\frac{F}{A}$$ (P = Pressure, F = normal force, A = Area)
(iii) P = h d g(P = Pressure, d = density, g = acceleration due to gravity)
(iv) T = $$\frac{F}{l}$$ (F = the total force acting as an imaginary line of length l, drawn tangentially on the liquid surface at rest, the force of surface tension T)
(v) E = T × a (E = Surface energy, T = Surface tension, a = area)
(vi) P = $$\frac{2T}{R}$$ (P = excess of pressure inside the liquid drop,
T = surface tension of the liquid,
R} = radius of the water drop)
(vii) Stress = $$\frac{\text { external deforming force on the body }}{\text { area of cross-section of the body }}$$
(viii) $$\frac{\text { Stress }}{\text { Strain }}$$ = constant
(ix) Poisson’s ratio = $$\frac{\text { lateral strain }}{\text { longitudinal strain }}$$
(x) $$\frac{P}{\rho g}+h+\frac{v^2}{2 g}$$ = constant (For the streamline flow of an ideal fluid of density \rho and passing any cross-section at a height h with a velocity v at pressure P and acceleration due to gravity is g)
(xi) Excess pressure inside a soap bubble (P) =
$$\frac{4 T}{R}$$(T = surface tension of liquid R = radius of the liquid bubble)
(xii) F = $$\frac{Y a l}{L}$$
(F = external tensile force, Y = longitudinal stress, L = length of wire ; a = cross-section, l = elongated by length)

Example 1 : A water filled cone of height 50 cm and the base area of 20 cm 2 is placed on a table with the base on the table. What is the thrust offered by the water on the table?
h = 50 cm
d = 1 gcm-3
g = 980 cms-2
A = 20 cm2
Thrust = Pressure × area = h d g × A
∴ Thrust
= 50 × 1 × 980 × 20
= 9.8 × 105 dyne
= 9.8 N

Example 2 : The pressure of air in a soap bubble of 0 . 7 cm diameter is 8 mm of water above the atmospheric pressure. Calculate the surface tension of the soap solution.
P = 8 mm = 0.8 cm
r = 0.7 cm / 2 = 0.35 cm
The excess of pressure inside a soap bubble is given by
P = $$\frac{4 T}{r}$$
∴ T = $$\frac{P r}{4}$$
= $$\frac{0.8 × 980 × 0.35}{4}$$
= 686 dyne cm-1

Example 3: Surface tension of water is 0.072 Nm-1. Calculate the excess pressure inside a water drop of diameter 1.2 mm.
T = 0.072 Nm-1
d = 1.2 mm = 1.2 × 10-3 m
P = $$\frac{2 T}{r}$$ = $$\frac{4 T}{d}$$
= $$\frac{4 \times 0 \cdot 072}{1.2 \times 10^{-3}}$$
= $$\frac{4 × 0.072}{1 . 2 × 10^{-3}}$$
= 240 Nm-2

Example 4 : one end of an iron wire of length 250 cm of diameter 1 mm is rigidly fixed with a beam and a weight of 8 kg} is placed at the other end. Calculate the elongation of the wire.
(Y. of iron = 20 × 1011 dyne cm-2 ; g = 9.8 ms-2)
L = 250 cm = 2.5 m
d = 1 mm = 10-3m
W = 8 kg . wt
Y = 20 × 1011 dyne cm-2
= 2.0 × 1011 Nm-2
g = 9.8 ms-2
l = ?
l = $$\frac{F L}{A}$$

= 0.125 × 10-2 m

Example 5 : Find the pressure at a depth of 5 m below the surface of a lake. (Density of water = 1000 kgm-3).
h = 5 m
d = 1000 kgm-3
g = 9.8 ms-2
p = ?
P = hdg
P = 5 × 1000 × 9.8
Or,
= 4.9 × 104 Nm-2

Example 6 : Atmospheric pressure at a place is 750 mm. Find the pressure at the place. (Given density of mercury = 13.6 g / cc and g = 980 cm/s2)
h = 750 mm = 75 mm
d = 13.6 g / cc
g = 980 cm / s2
p = ?
P = hdg
= 75 × 13.6 × 980
= 0.9995 × 106 dyne/cm2

Example 7 : A body having volume of 50 cm 3 weighs 0.5 kg in air. Find its density.
m = 0.5 kg
v = 50 cm
= 50 × 10-6 m3
D = ?
Density of the body (D) = $$\frac{m}{v}$$
= $$\frac{0.5}{50 × 10^{-6}}$$
= 104 kgm-3

Example 8 : Relative density of silver is 10.5 Find the density of silver.
Given, relative density of silver = 10.5
Now, relative density of silver = $$\frac{\text { density of silver }}{\text { density of water }}$$
∴ density of silver
= relative density of silver × density of water
= 10.5 × 1000 = 10500 kgm-3

Example 9 : A block of 36 cc. ice floats on water. What volume of it remains above water surface?
It is known that nearly $$\frac{1}{12}$$ part of the volume of an ice block remains above water when it floats on water.
Here total volume of the ice block is 36 cc.
∴ $$\frac{1}{12}$$ of 36 cc = 3 cc
So, 3 cc of ice remains above water surface.

Example 10 : Gold has density 19.3 g/cc. An ornament weighs 5.80 g in air and 5.25 g in water. Is the ornament made of pure gold ?
From Archimedes’ principle we get, volume of the ornament = (5.80 – 5.25) cc = 0.55 cc.
Now, considering density of pure gold 19.3 g / cc, the weight of the ornament in air = (19.3 × 0.55) g-wt. = 10.615 wt. But as indicated in the problem, weight of the ornament in air is 5.80 g-wt. Hence, the ornament is not made of pure gold.

Example 11 :
A metallic wire of length 60 cm when stretched along length by a normal force becomes 61 cm Find the longitudinal strain.
Given, original length of wire, l = 60 cm
final length of the wire, l’ = 61 cm
increase in length Δ l = l’-1 = (61-60)
cm = 1
∴ longtudinal strain = $$\frac{\Delta l}{l}$$ = $$\frac{1}{60}$$ = 0 . 017

Example 12 : A metallic wire of radius 0.1 cm and length 2 m is extended by a weight of 2.5 kg. Find the normal stress set up.
Given external deforming
force, F = 2.6 kg-wt = 2.5 × 9.8 N
radius of the wire, r = 0 . 1 cm
= 0.1 × 10-2 m
area of cross-section of the wire = π r2 = π(10-3)2 m2
Since normal stress = $$\frac{\text { external deforming force }}{\text { area }}$$
= $$\frac{2.5 × 9.8}{\pi(10^{-3})^2}$$
= 7.8 × 106 Nm-2

Example 13 :
The ratio radiis of two wires of same material is 2: 1. If these wires are stretched by equal force, find the ratio of stresses produced in them.
Stress (S) = $$\frac{\text { force }}{\text { area }}$$ = $$\frac{F}{\pi \sigma^2}$$ or, s α $$\frac{1}{r^2}$$
∴ $$\frac{S_1}{S_2}$$ = $$\frac{r_2^2}{r_1^2}$$ = $$(\frac{1}{2})^2$$ = $$\frac{1}{4}$$