Chapter 3 – Matter: Structure and Properties | Chapter Solution Class 9

Publisher	: Santra publication pvt. ltd.
Book Name	: Madhyamik Physical Science And Environment
Class	: 9 (Madhyamik)
Subject	: Physical Science
Chapter Name	: Matter: Structure and Properties

Multiple choice questions (MCQ)

Question 1 

Dimension of density is

1. ML^-2
2. ML^-3
3. LT^-3
4. ML^-4

Answer

ML^-3

Explanation

The dimension of density is ML^-3, which represents mass per unit volume.

Question 2

SI unit of pressure is

1. N
2. N/m²
3. N.m
4. N/m

Answer

N/m²

Explanation

The SI unit of pressure is N/m², which is commonly known as Pascal (Pa).

Question 3

A body floats in a liquid contained in a beaker. The whole system falls freely under gravity. The upward thrust on the body due to the liquid then is

1. Zero
2. equal to the liquid displaced
3. equal to the weight of the body in the air
4. equal to the weight of the immersed portion in the liquid

Answer

equal to the liquid displaced

Explanation

The body is floating in the liquid, which means that it displaces a certain volume of the liquid. When the system falls freely under gravity, the buoyant force acting on the body due to the liquid will still be equal to the weight of the fluid displaced by the body.

Question 4

Clouds float in the atmosphere on account of their

1. low viscosity
2. low density
3. low temperature
4. creation of low pressure

Answer

low density

Explanation

Clouds are formed when warm, moist air rises and cools, causing the water vapour in the air to condense into liquid droplets or ice crystals. These droplets or crystals are much denser than the surrounding air, which makes them fall towards the ground due to gravity.

Question 5

After terminal velocity to reached, the acceleration of a body falling through a fluid is

1. equal to g
2. zero
3. less than g
4. more than g

Answer

zero

Explanation

When an object is dropped in a fluid, it experiences a drag force that opposes its motion. Initially, the object accelerates due to the gravitational force, but as the speed of the object increases, the drag force also increases until it becomes equal and opposite to the gravitational force. At this point, the net force acting on the object becomes zero, and it stops accelerating.

Question 6

The property by virtue of which a fluid tries to prevent the relative motion between adjacent layers is called

1. Elasticity
2. Rigidity
3. viscosity
4. cohesion

Answer

viscosity

Explanation

Viscosity is a measure of a fluid’s resistance to flow. It arises due to the cohesive forces between the molecules of the fluid, which cause them to exert a drag force on each other when the fluid is in motion. This drag force leads to internal friction within the fluid, which resists the relative motion between adjacent layers of the fluid.

Question 7

The pressure energy per unit when of a liquid is

1. p/ρ
2. P
3. P.ρ
4. ρ/p

Answer

p/ρ

Explanation

Pressure is defined as force per unit area, and its SI unit is the Pascal (Pa). Density is defined as mass per unit volume, and its SI unit is kg/m³. Therefore, the unit of pressure energy per unit volume is the Joule per cubic meter (J/m³).

Question 8

Which one of the following substances has the greatest viscosity?

1. water
2. mercury
3. oxygen
4. hydrogen

Answer

Mercury

Explanation

Viscosity is a measure of a fluid’s resistance to flow. It arises due to the cohesive forces between the molecules of the fluid, which cause them to exert a drag force on each other when the fluid is in motion. A fluid with a high viscosity will be thicker and more resistant to flow than a fluid with a low viscosity.

Question 9

A drop of liquid assumed a spherical shape because of

1. density
2. viscosity
3. granitization
4. surface tension

Answer

surface tension

Explanation

Surface tension is the property of a liquid that allows it to resist external forces that distort its surface. It arises due to the cohesive forces between the molecules of the liquid, which create a thin film at the surface of the liquid. This film acts as an elastic membrane that tries to minimize the surface area of the liquid.

Question 10

Within the elastic limit, stress is

1. zero
2. independent of strain
3. directly proportional to strain
4. inversely proportional to strain

Answer

directly proportional to strain

Explanation

Stress is defined as the force per unit area and is given by the formula stress = force/area. It is a measure of the internal forces that act within a material when it is subjected to an external force.

Question 11

The modulus of elasticity is dimensionally equivalent

1. stress
2. strain
3. surface tension
4. acceleration

Answer

stress

Explanation

The modulus of elasticity, also known as Young’s modulus, is a material property that describes the stiffness of the material. It is defined as the ratio of stress to strain within the elastic limit of the material.

Question 12

According to Hooke’s law of elasticity, if stress is increased the ratio of stress to strain

1. increase
2. decreases
3. becomes zero
4. remains constant

Answer

remains constant

Explanation

Hooke’s law states that within the elastic limit of a material, the stress applied to the material is directly proportional to the strain produced.

Answer in one word or in one sentence

[Each of Mark-1]

Question

1. Is thrust a scalar or a vector quantity? 
2. If the specific gravity of steel is 7.82 then what is its density in S.I?
3. In which direction Buoyancy acts?
4. Does Archimede’s principle hold in the case of gases?
5. What does a sudden fall in barometric height indicate?
6. What is the density of pure water in SI?
7. A cork is floating in the water; what is its apparent weight?
8. How many types of fluid motion are seen?
9. Name one characteristic of an ideal flid.
10. What is the significance of Critical velocity in the discussion of fluid motion?
11. From which conservation law of physics we can arrive at Bernoulli’s theorem?
12. How does the viscous drag on a moving spherical body vary with its velocity?
13. Does surface tension act within the inside of a liquid?
14. Name practical application of spreading liquid over solid.
15. What is the SI unit of stress?
16. What is the dimension of the force constant of a spring?
17. What is more elastic rubber or steel?
18. Why strain has no unit?
19. What is the SI unit of Young’s modulus?
20. What will happen to the potential energy if a wire is compressed?

Answer

1. Vector
2. 7820 kg/m³
3. Upward
4. Yes
5. Bad weather or a storm is coming
6. 1000 kg/m³
7. Its weight is equal to the weight of the water it displaces
8. Fluid flow occurs in three possible ways: turbulent, laminar, and transition regions.
9. Zero viscosity and turbulence, incompressible
10. It marks the transition from laminar to turbulent flow
11. Conservation of energy
12. Viscous drag increases with velocity
13. No, surface tension acts at the surface of a liquid.
14. Adhesion, wetting, capillary action, inkjet printing.
15. Pascal (Pa)
16. [ML⁰T^-2]
17. Steel
18. Strain is a ratio of two lengths, so it’s a dimensionless quantity.
19. Pascal (Pa)
20. Potential energy will increase

Answer the following question (Short answer type)

[Each of Mark-2]

Question 1

Define density and relative density. Distinguish between them.

Answer

Density: It is defined as the mass of an object divided by its volume. The SI unit of density is kilograms per cubic meter (kg/m³).

Relative density: It is a dimensionless quantity, as it is a ratio of two densities with the same units.

Density	Relative Density
Mass per unit volume of a substance	The ratio of the density of a substance to the density of a reference substance
Density = Mass / Volume	Relative Density = Density of substance / Density of reference substance

Question 2

What do you understand by the pressure and thus on a surface immersed in a liquid? Things can be cut by the sharp edge of a knife easily but cannot be cut blunt edge Explain.

Answer

Pressure on a surface immersed in a liquid is the force exerted by the liquid per unit area of the surface. It is directly proportional to the depth of the surface below the liquid surface and the density of the liquid.

A sharp edge of a knife can cut things easily because it concentrates the force on a small area, increasing the pressure applied to the object. In contrast, a blunt edge distributes the force over a larger area, decreasing the pressure applied to the object, which makes it harder to cut.

Question 3

What is buoyancy? Show how and on what factor its value depends.

Answer

Buoyancy is the upward force exerted by a fluid on a body immersed in it. The value of buoyancy depends on the volume of the displaced fluid, the density of the fluid, and the gravitational force acting on the fluid and the body. Archimedes’ principle states that the buoyant force is equal to the weight of the displaced fluid.

Question 4

State Archimedes’ principle. Discuss the conditions of the flotation of a body.

Answer

Archimedes’ principle states that a body fully or partially immersed in a fluid experiences an upward force that is equal in magnitude to the weight of the fluid it displaces.

The conditions of the flotation of a body are

• For a body to float in a fluid, the buoyant force acting on the body must be equal to the weight of the body.
• The buoyant force is equal to the weight of the fluid displaced by the body.

Question 5

Give reason: A ship made of iron floats in water but a piece of rail sinks.

Answer

A ship made of iron floats in water because its overall density is less than the density of water. The ship is designed to displace a large volume of water, which generates a buoyant force that is greater than the weight of the ship. In contrast, a piece of rail is more dense than water, so it sinks. The buoyant force acting on the rail is not sufficient to counteract its weight, causing it to sink.

Question 6

Explain how a submarine can both float and travel submerged underwater.

Answer

A submarine can float on the surface by filling its ballast tanks with air and can submerge by filling them with water. It can travel underwater using a propulsion system and can control its depth by adjusting the water level in the ballast tanks, making it more or less dense than water.

Question 7

What are the circumstances in which a siphon does not work?

Answer

The circumstances in which a siphon does not work are

• The highest point of the siphon must be lower than the surface of the liquid being siphoned.
• The siphon tube must be airtight and free from leaks.
• The liquid being siphoned must be denser than the liquid in the receiving container.

Question 8

What would you conclude if the height of the mercury column decreased abruptly?

Answer

If the height of the mercury column in a barometer decreases abruptly, it could indicate:

• A decrease in atmospheric pressure due to a weather system moving through the area.
• A decrease in the elevation of the barometer, such as when it is moved to a lower altitude.

Question 9

What is meant by streamline flow?

Answer

Streamline flow refers to the smooth flow of a fluid in parallel layers that do not mix with each other. The fluid particles move in a continuous and orderly fashion without turbulence or irregularities, resulting in the formation of streamlined patterns.

Question 10

What is meant by turbulent flow and when the fluid flow becomes turbulent?

Answer

Turbulent flow: If the path of the particle of a moving fluid is completely irregular and random, the flow of the fluid is said to be a turbulent flow.

Whenever the Reynolds number is less than about 2,000, flow in a pipe is generally laminar, whereas, at values greater than 2,000, flow is usually turbulent.

Question 11

What is a viscous force and on what factors does it depend?

Answer

Viscous force, also known as drag force, is a force that opposes the motion of an object through a fluid.

The amount of viscous force depends on several factors, including:

1. The viscosity of the fluid.
2. The density of the fluid.
3. The temperature of the fluid.

Question 12

How does the rate of flow of a liquid through a capillary tube change with its radius?

Answer

According to the Hagen-Poiseuille equation, the rate of flow of a liquid through a capillary tube is directly proportional to the fourth power of the radius of the tube. A larger radius allows for more space for the liquid to flow, reducing friction and increasing the flow rate. A smaller radius results in less space, increasing friction and decreasing the flow rate.

Question 13

State Bernoulli’s theorem and write down its mathematical form.

Answer

Bernoulli’s theorem states that in a steady flow of an incompressible fluid, the total energy of the fluid remains constant along a streamline.

Mathematically, it is expressed as P + (1/2)ρv² + ρgh = constant, where P is the pressure, ρ is the density, v is the velocity, h is the height above a reference point, and g is the acceleration due to gravity.

Question 14

Why raindrops fall with uniform velocities through the atmosphere?

Answer

Raindrops fall with uniform velocities through the atmosphere due to air resistance and gravitational force. As a raindrop falls through the atmosphere, it encounters air resistance, which increases as the speed of the drop increases. This air resistance ultimately balances the gravitational force, resulting in a constant velocity of the falling raindrop.

Question 15

Water flows faster than glycerine-Why?

Answer

Water flows faster than glycerine because water has a lower viscosity than glycerine. Viscosity is the measure of a fluid’s resistance to flow, and fluids with higher viscosities flow more slowly than those with lower viscosities. As glycerine has a higher viscosity than water, it flows more slowly.

Question 16

Why a liquid drop under no external force is always spherical in shape?

Answer

A liquid drop under no external force is always spherical in shape due to surface tension. Surface tension is the property of a liquid that causes the surface of the liquid to behave like a stretched elastic membrane.

Question 17

Why does the surface of a liquid act like a stretched membrane?

Answer

The surface of a liquid acts like a stretched membrane due to cohesive forces between the liquid molecules. These forces cause the molecules on the surface of the liquid to be pulled inwards, creating surface tension that resists any external force trying to stretch or break the surface.

Question 18

What is the effect of temperature on surface tension?

Answer

Surface tension generally decreases with increasing temperature due to increased molecular motion that breaks the cohesive forces between liquid molecules.

Question 19

Define stress and strain.

Answer

Stress is defined as the force acting on a unit area of a material and is expressed in units of pressure or force per unit area.

Strain is a dimensionless quantity and is usually expressed as a percentage or a fraction.

Question 20

State Hookes law?

Answer

Hooke’s law states that the force required to extend or compress a spring by a certain distance is proportional to that distance.

Mathematically, F = kx,

where F is the force, x is the displacement, and k is the spring constant, which is a measure of the stiffness of the spring.

Question 21

What is force constant of a spring and what property of the spring is expressed by it?

Answer

The force constant of a spring is a measure of its stiffness, defined as the force required to stretch or compress a spring by a unit distance. It is directly proportional to the spring’s resistance to deformation under an applied force. A larger force constant indicates a stiffer spring.

Question 22

Define Young’s modulus.

Answer

It is defined as the ratio of stress to strain under tensile or compressive loading and is a measure of the material’s ability to withstand deformation along an axis when subjected to a force in that direction.

Question 23

Define terminal velocity. On what facts does it depend?

Answer

Terminal velocity is the maximum velocity that an object reaches while falling through a fluid, such as air or water.

Terminal velocity depends on the following factors:

• The size, shape, and mass of the object falling through the fluid.
• The density and viscosity of the fluid through which the object is falling.
• The force of gravity acting on the object.

Long answer type of questions

[Each of Mark-3]

Question 1

Find an expression for pressure at a depth h inside a liquid of density d.

Answer

Consider a vessel containing a liquid of density ρ. Let the liquid be stationary. In order to calculate the pressure at a depth, consider a horizontal circular surface PQ of area A at a depth h below the free surface XY of the liquid. The pressure on the surface PQ will be due to the thrust of the liquid contained in cylinder PQRS of height h with PQ as its base and top face RS lying on the free surface XY of the liquid.

Total thrust exerted on the surface PQ

= Weight of the liquid column PQRS

= Volume of liquid column PQRS × density × g

= (Area of base PQ × height) × density × g

= (A × h) × ρ × g

This thrust is exerted on the surface PQ of area A. Therefore, pressure is given as shown below.

P = {Ahρg\over A} = hρg

Thus, Pressure = depth × density of liquid x acceleration due to gravity.

Question 2

State and explain Archimedes’ principle. What is buoyancy? Mention the factors on which buoyancy depends. 

Answer

Archimedes’ principle states that an object immersed in a fluid experiences an upward buoyant force that is equal to the weight of the fluid displaced by the object. This principle can be explained by the fact that the pressure at the bottom of the object is greater than the pressure at the top, resulting in a net upward force.

Buoyancy is the upward force exerted by a fluid on an object that is partially or completely immersed in it.

Buoyancy depends on the following factors:

• The density of the fluid in which the object is immersed.
• The volume of the object that is submerged in the fluid.

Question 3

What is a siphon? Explain its principle of action.

Answer

A siphon is a bent tube used to transfer liquid from one container to another, where the liquid flows uphill against gravity.

Principle of action of a siphon

The principle of a siphon is based on the fact that liquid flows from a higher level to a lower level due to the difference in pressure between the two points. When the siphon tube is filled with liquid and the ends are placed in two containers, the liquid flows down the tube due to the force of gravity until the lowest point of the siphon tube is reached. At this point, the liquid is pulled up and over the curve of the tube by the difference in pressure between the higher and lower points and flows into the other container until both liquid levels are equal.

Question 4

Describe with a diagram the principle of action of a Fortins barometer. How does a barometer help to forecast the weather?

Answer

A Fortin barometer is a type of mercury barometer used to measure atmospheric pressure. It works based on the balance between the atmospheric pressure pushing down on the mercury in the cistern and the weight of the column of mercury in the tube, which rises until it reaches an equilibrium with the atmospheric pressure.

A barometer helps to forecast the weather by:

• Measuring changes in atmospheric pressure.
• A sudden drop in pressure indicates the approach of a low-pressure system and usually signifies cloudy and rainy weather.
• A rise in pressure indicates the approach of a high-pressure system and usually signifies clear and sunny weather.
• By monitoring changes in atmospheric pressure, meteorologists can forecast changes in weather patterns.

Question 5

On the basis of which principle town water supply system works? Describe the working principle briefly.

Answer

The town water supply system works on the principle of gravity and pressure. Water is stored in a water tower, which is usually located at a high point in the town. The water in the tower is held at a higher elevation than the surrounding town, creating a potential energy difference. This potential energy difference generates pressure that pushes the water through the pipes and into homes and businesses.

When a tap is opened, the pressure difference between the water in the pipes and the atmospheric pressure causes the water to flow out of the tap.

Question 6

What is an Artesian well? Explain its principle of working with the help of a diagram.

Answer

Below the surface of the Earth, there exist concave-shaped layers, some of them are pervious and others are impervious to water. The water layer lying between two impervious layers extends up to the surface of the Earth and the surface water percolates through the previous layers and fills the concave layers with water. Now when a bore is made at the middle of the layer, water comes out through the bore with a great speed because the two ends of the water-filled concave layers are at a higher level than the middle and thus it makes a high pressure at the middle due to the fact that ‘water finds its own level’. As this kind of well was found first in the province of Artois in France and hence it is known as an ‘Artesian well’.

Question 7

Write down the characteristics of liquid pressure.

Answer

The characteristics of liquid pressure include:

• Liquid pressure is exerted equally in all directions.
• Liquid pressure increases with depth and is directly proportional to the density of the liquid.
• Liquid pressure is transmitted undiminished in a confined liquid.
• Liquid pressure is independent of the shape of the container but depends on the height and density of the liquid.

Question 8

What is a viscous force? How does it originate?

Answer

Viscous force is the force that opposes relative motion between adjacent layers of fluid that are in contact with each other.

It originates from the internal friction between the molecules of the fluid. When layers of fluid move relative to each other, the molecules in one layer interact with the molecules in the adjacent layer. These interactions create attractive and repulsive forces between the molecules, which resist the motion of the layers and generate the viscous force.

Question 9

What is meant by streamlining the flow and laminar flow? Is the streamlined flow of a fluid through a tube laminar? Explain

Answer

Streamlining the flow refers to reducing the resistance and turbulence of a fluid (liquid or gas) as it moves through a conduit, such as a pipe or a channel.

Laminar flow is a type of flow characterized by smooth, predictable movement of fluid layers in parallel paths, without turbulence or mixing.

The streamlined flow of a fluid through a tube can be laminar if the conditions are right, i.e., the fluid has a low velocity, the tube is straight and smooth, and the fluid’s viscosity is high enough to prevent turbulence.

Question 10

State Bernoulli’s theorem. Write down its mathematical expression. What are its limitations?

Answer

Bernoulli’s theorem states that in an ideal fluid flow, where there is no friction or energy loss, the sum of the pressure energy, kinetic energy, and potential energy at any point along a streamline is constant.

Mathematically, this can be expressed as:

P + (1/2)ρv² + ρgh = constant

Some of the limitations of Bernoulli’s theorem include:

1. It applies only to ideal fluids that are incompressible and have no viscosity.
2. It assumes that the flow is steady and the fluid is incompressible.

Question 11

What do liquid surfaces tend to keep their surface area minimum Discuss with some examples. Mention the factors on which surface tension depends.

Answer

Liquid surfaces tend to keep their surface area minimum due to surface tension, which is the force that causes the surface of a liquid to behave like an elastic membrane. For example, when a drop of water is placed on a flat surface, it forms a sphere to minimize its surface area. Soap bubbles and oil droplets in water also exhibit this behavior due to surface tension.

The surface tension of a liquid depends on the following factors:

1. Intermolecular forces between molecules of the liquid.
2. The size of the molecules or atoms that make up the liquid.
3. The temperature of the liquid.

Question 12

State and explain Hooke’s law. Define longitudinal stress, longitudinal strain and Young’s modulus.

Hooke’s law states that the force required to extend or compress a spring by a distance is directly proportional to that distance. In other words, the more you stretch or compress a spring, the more force it will require. This relationship is known as the spring constant, and it is a measure of the stiffness of the spring. Hooke’s law is used to describe the behavior of springs and other elastic materials.

• Longitudinal stress: The stress that occurs when a force is applied in the longitudinal direction of a material, causing it to elongate or compress.
• Longitudinal strain: The resulting deformation of a material caused by the application of longitudinal stress.
• Young’s modulus: A measure of the stiffness of a material, defined as the ratio of longitudinal stress to longitudinal strain.

Numerical problems

Question 1

A force of 100N is applied to an object of area 2 m² to calculate the pressure [Ans. 50 N/m²]

Answer

Force (F) = 100 N

Area (A) = 2 m²

Pressure (P) = Force\over Area

= 100\over 2

= 50 N/m²

Question 2

An actress of mass 50 Kg is wearing sharp-heeled shoes. If the area of one heel is 1 cm², Calculate the pressure exerted on the ground when she stands on just one heel (g = 10 m/s²) [Ans. 5 × 10⁶ Pa]

Answer

Mass (m) = 50 Kg

Area (A) = 1 cm² = 10^-4 m²

Step 1: Calculation of Force

Force (F) = Mass (m) × g

= 50 × 10 = 500 N

Step 2: Calculation of Pressure

Pressure (P) = Force\over Area

= 500\over 10^{-4}

= 5 × 10⁶ Pascal

Question 3

What are the pressure and total thrust on the bottom of a cylindrical vessel of diameter 0.28 m containing 30.8 litres of mercury? (density of mercury = 13.6 × 10³ Kg/m³) [Ans. 66.64 × 10³ N/m², 4.1 × 10³ N]

Answer

Diameter (d) = 0.28 m

Volume (V) = 30.8 L = 0.0308 m³

Step 1: Calculation of Area of base

Area = πr²

= 22\over 7 × 0.14²

= 0.0616 m²

Step 2: Calculation of Thrust

Thrust (F) = Mass × g

= Volume × density × g

= 0.0308 × 13.6 × 10³ × 10

= 4100 N

Step 3: Calculation of Pressure

Pressure (P) = Thrust\over Area

= 4100\over 0.0616

= 66558.44 Pa or 6.65 × 10⁴ Pa

Question 4

The density of water is 1000 kg/m³. If the relative density of iron is 7.874 calculate the density of iron [Ans. 7874 kg/m³]

Answer

Density of water = 1000 kg/m³

Relative density (RD) = 7.874

Density of iron = Density of water × (RD)

= 1000 × 7.874 = 7874 kg/m³

Question 5

An oil of relative density 1.2 and volume 1 litre is poured into water to find the mass of the oil [Ans. 1.2 kg]

Answer

RD of oil = 1.2

Density of water = 1 g/cm³

Volume of oil (V) = 1 lt = 1000 cm³

Step 1: Calculating the density of oil

Density of oil = Density of water × (RD)

= 1 × 1.2 = 1.2 g/cm³

Step 2: Calculating the mass of oil

Mass of oil = Volume of oil × density

= 1000 × 1.2 = 1200 g or 1.2 Kg

Question 6

The density of aluminium is 2700 kg/m³. Find the relative density of aluminium Given that the density of water = 10³ kg/m³ [Ans. 2.7]

Answer

Density of aluminium = 2700 kg/m³

Density of water = 1000 kg/m³

Relative Density (RD) = 2700\over 1000 = 2.7

Question 7

The volume of a solid of mass 500g is 350 cc

1. What will be the density of the solid?
2. What will be the mass of water displaced by this solid?
3. What will be the relative density of the solid?
4. Will it float or sink in water?

[Ans. (a) 1.42 g/cc (b) 350 g (c) 1.42 (d) it will sink in water]

Answer

Mass (m) = 500 g

Volume (V) = 350 cc

(a) Density = 500\over 350 = 1.42 g/cc

(b) The solid will displace water equal to its own volume.

The volume of water displace = 350 cc

Mass = volume × density

= 350 × 1 = 350 g

(c) Relative Density = 1.42\over 1 = 1.42

(d) Since the relative density of the solid (1.42) is greater than the relative density of water, therefore, the solid is heavier than water and hence it will sink in water.

Question 8

A load of 25 kg isattached to a of diameter 0.4 cm and a length of 100 cm of the wire is found to elongate to 102 cm. Find Young’s modulus for the material of the wire. [Ans. 0.975 × 10¹⁰ dyne/cm²]

Answer

Mass (m) = 25 kg

Original length (l) = 100 cm = 1 m

Force = m × g = 25 × 9.8 = 245 N

Diameter (d) = 0.4 cm = 0.4 × 10^-2 m

Change in length (Δl) = 102 – 100 = 2 cm or 0.02 m

Step 1: Calculation of Area

Area = πr²

= 22\over 7 × (0.2 × 10^-2)²

= 1.257 × 10^-5 m²

Step 2: Calculation of stress

Stress = Force \over Area

= 245 \over 1.257 × 10^{-5}

= 1.95 × 10⁷ N/m²

Step 3: Calculation of strain

Strain = Δl \over l

= 0.02 \over 1 = 0.02

Step 4: Calculation of Young modulus

Young modulus = stress \over strain

= 1.95 × 10^7\over 0.02

= 9.744 × 10⁸ N/m²

= 9.744 × 10^8 × 10^5 \over 10^{-4} dyne/cm²

= 0.975 × 10¹⁰ dyne/cm²

Question 9

A stress of 9.8 × 10⁶ N/m² is applied to a wire and which Young’s modulus is 10¹¹ N/m² find the percentage increase in length [Ans. 0.0098%]

Answer

Stress = 9.8 × 10⁶ N/m²

Young’s modulus = 10¹¹ N/m²

Young modulus = stress \over strain

⇒ strain = stress \over Young\ modulus

⇒ strain = 9.8 × 10^6 \over 10^11

⇒ Δl\over l = 0.000098

Percentage increase in length = Δl\over l×100

= 0.000098 × 100

= 0.0098 %