Explore the complete solved exercise of Chapter 6 – Mechanical Properties of Matter from 9th Class Physics. Simplified solutions with detailed explanations for students of the Federal Board and other boards.
MCQs
6.1
Statement: A wire is stretched by a weight WW. If the diameter of the wire is reduced to half of its previous value, the extension will become:
Options:
(a) One-half
(b) Double
(c) One-fourth
(d) Four times
Answer: (d) Four times
Explanation:
The extension of a wire is given by the formula:
ΔL∝1/d2
where dd is the diameter of the wire. Reducing the diameter to half means d′=d/2. Substituting, the extension becomes:
ΔL′=ΔL×1/(1/2)2=4ΔL
Thus, the extension increases fourfold.
Tip: Remember that wire extension depends inversely on the square of its diameter.
6.2
Statement: Four wires of the same material are stretched by the same load. Their dimensions are given below. Which of them will elongate most?
Options:
(a) Length 1 m, Diameter 1 mm
(b) Length 2 m, Diameter 2 mm
(c) Length 3 m, Diameter 3 mm
(d) Length 4 m, Diameter 0.5 mm
Answer: (d) Length 4 m, Diameter 0.5 mm
Explanation:
The elongation is directly proportional to the length and inversely proportional to the square of the diameter:
ΔL∝L/d2
Substitute the values for each option to find the highest elongation. Option (d) has the largest L/d2 ratio.
Tip: For such questions, focus on maximizing the L/d2 value.
6.3
Statement: Two metal plates of area 2 and 3 square meters are placed in a liquid at the same depth. The ratio of pressures on the two plates is:
Options:
(a) 1:1
(b) √2: √3
(c) 2:32:3
(d) 4:9
Answer: (a) 1:1
Explanation:
Pressure in a liquid depends only on depth and density, not on area. Since both plates are at the same depth, the pressures are equal.
Tip: Pressure P=ρgh. Area doesn’t influence pressure.
6.4
Statement: The pressure at any point in a liquid is proportional to:
Options:
(a) Density of the liquid
(b) Depth of the point below the surface of the liquid
(c) Acceleration due to gravity
(d) All of the above
Answer: (d) All of the above
Explanation:
Pressure in a liquid is given by:
P=ρgh
where ρ is density, g is gravitational acceleration, and h is depth.
Tip: Memorize the pressure formula and identify the variables.
6.5
Statement: Pressure applied to an enclosed fluid is:
Options:
(a) Increased in proportion to the surface area of the fluid
(b) Diminished and transmitted to the walls of the container
(c) Increased in proportion to the mass of the fluid and transmitted to each part of the fluid
(d) Transmitted unchanged to every portion of the fluid and walls of the container
Answer: (d) Transmitted unchanged to every portion of the fluid and walls of the container
Explanation:
This is Pascal’s law, which states that pressure in an enclosed fluid is distributed equally in all directions.
Tip: Always associate enclosed fluid systems with Pascal’s law.
6.6
Statement: The principle of a hydraulic press is based on:
Options:
(a) Hooke’s law
(b) Pascal’s law
(c) Principle of conservation of energy
(d) Principle of conservation of momentum
Answer: (b) Pascal’s law
Explanation:
A hydraulic press works by transmitting pressure equally through a fluid to generate a large force.
Tip: Hydraulic systems are practical examples of Pascal’s law.
6.7
Statement: When a spring is compressed, what form of energy does it possess?
Options:
(a) Kinetic
(b) Potential
(c) Internal
(d) Heat
Answer: (b) Potential
Explanation:
When a spring is compressed or stretched, it stores energy as elastic potential energy:
U=12kx2
Tip: Elastic energy is always potential.
6.8
Statement: What is the force exerted by the atmosphere on a rectangular block surface of length 50 cm and breadth 40 cm? The atmospheric pressure is 100 kPa.
Options:
(a) 20 kN
(b) 100 kN
(c) 200 kN
(d) 500 kN
Answer: (b) 100 kN
Explanation:
Force is given by:
F=P×A
Convert dimensions to meters: A=0.5×0.4=0.2 m2
Substitute P=100 kPa=100,000 Pa
F=100,000×0.2=20,000 N=20 kN
Tip: Always convert to SI units before solving.
C.6.1
Question:
A spring having spring constant k hangs vertically from a fixed point. A load of weight L, when hung from the spring, causes an extension x, provided the elastic limit of the spring is not exceeded.
Some identical springs, each with spring constant k, are arranged as shown below.
For each arrangement, complete the table by determining:
(i) The total extension in terms of x.
(ii) The spring constant in terms of k.
Understanding the problem:
- The spring constant k tells how stiff the spring is. The larger the value, the harder it is to stretch.
- When springs are combined (in series or parallel), their effective spring constant changes.
- We are asked to find the total extension xx and the effective spring constant for each arrangement.
Arrangement 1: Single Spring
- Total extension (x):
Only one spring is used, so the total extension xx remains the same as given. - Effective spring constant (keff):
The effective spring constant is the same as kk because there’s just one spring.
| Arrangement | Total Extension (xx) | Spring Constant (keff) |
|---|---|---|
| Single spring | x | k |
Arrangement 2: Two Springs in Series
- Total extension (x):
When springs are in series, the extension is shared by both. The total extension becomes: xtotal=x+x=2x - Effective spring constant (keff):
The formula for springs in series is: 1keff=1k+1k=2k - Solve for keff keff=k/2
| Arrangement | Total Extension (xx) | Spring Constant (keff) |
|---|---|---|
| Two springs in series | 2x | k/2 |
Arrangement 3: Two Springs in Parallel
- Total extension (x):
In parallel, the load is shared equally by both springs, so each spring stretches only half as much as a single spring. The total extension is: xtotal=x/2 - Effective spring constant (keff}):
The formula for springs in parallel is: keff=k+k=2k
| Arrangement | Total Extension (xx) | Spring Constant (keff) |
|---|---|---|
| Two springs in parallel | x/2 | 2k |
Final Answer:
| Arrangement | Total Extension (x) | Spring Constant (keff) |
|---|---|---|
| Single spring | x | k |
| Two springs in series | 2x | k/2 |
| Two springs in parallel | x/2 | 2k |
Explanation for Students:
- Series combination: Springs share the same force, but their extensions add up, making the effective spring weaker (keff < k).
- Parallel combination: Springs share the load, reducing the extension. The system becomes stiffer (keff} > k).
Tips:
- For series, use 1keff=1k/1+1k/2
- For parallel, add spring constants directly: keff=k1+k
6.2 Why are springs made of steel instead of iron?
Springs are made of steel instead of iron because steel is more elastic and can return to its original shape after stretching or compressing.
6.3 Which of the following materials is more elastic?
(a) Iron
(b) Air or water
Answer: (a) Iron is more elastic than air or water because it can return to its original shape after force is removed.
6.4 How does water pressure one meter below the surface of a swimming pool compare to water pressure one meter below the surface of a very large and deep lake?
Water pressure increases with depth. However, at the same depth (one meter), the pressure is the same in both the swimming pool and the lake because pressure depends on depth and not the size of the water body.
6.5 What will happen to the pressure in all parts of a confined liquid if pressure is increased on one part? Give an example from daily life where this principle is applied.
According to Pascal’s Law, if pressure is applied to one part of a confined liquid, it is transmitted equally in all directions.
Example: When we press a toothpaste tube from one end, the paste comes out from the nozzle evenly.
6.6 If some air remains trapped within the top of the mercury column of the barometer, which is supposed to be a vacuum, how would it affect the height of the mercury column?
If air is trapped, it will exert pressure and reduce the height of the mercury column, giving incorrect atmospheric pressure readings.
6.7 How does the long neck of a giraffe not cause a problem when it raises its neck suddenly?
A giraffe has special blood vessels and valves in its neck that control blood flow, preventing sudden pressure changes and protecting the brain from excess or low blood pressure.
6.8 The end of the glass tube used in a simple barometer is not properly sealed, and some leak is present. What will be its effect?
If the glass tube is not properly sealed, air will enter, affecting the vacuum at the top. This will cause the mercury level to drop, leading to incorrect atmospheric pressure readings.
6.9 Comment on the statement, “Density is a property of a material, not the property of an object made of that material.”
Density is a property of a material, meaning that it remains the same regardless of the object’s size or shape. For example, the density of iron is the same whether it is a small nail or a large iron rod.
6.10 How is the load of a large structure estimated by an engineer?
Engineers estimate the load of large structures using principles of pressure, force distribution, and material strength. They calculate how much weight a structure can support without breaking or collapsing.
Comprehensive Questions and Answers
6.1 What is Hooke’s Law? Give three applications of this law.
Hooke’s Law states that the force needed to stretch or compress a spring is directly proportional to the distance it is stretched or compressed.
Applications:
- Used in vehicle suspension systems to absorb shocks.
- Used in measuring forces using spring balances.
- Helps in designing strong buildings and bridges.
6.2 Describe the working and applications of a simple mercury barometer.
A mercury barometer is a device used to measure atmospheric pressure. It consists of a long glass tube filled with mercury, inverted in a dish of mercury. The height of the mercury column indicates the atmospheric pressure.
Applications:
- Used in weather forecasting.
- Helps in measuring altitude.
- Used in scientific experiments to study pressure changes.
6.3 Describe Pascal’s Law. State its applications with examples.
Pascal’s Law states that when pressure is applied to a confined fluid, it is transmitted equally in all directions.
Applications:
- Hydraulic brakes – Used in vehicles for smooth braking.
- Hydraulic lifts – Used to lift heavy objects, such as cars in service stations.
- Syringes – Used in medical injections to push liquid into the body.
6.4 On what factors does the pressure of a liquid in a container depend? How is it determined?
The pressure of a liquid in a container depends on:
- Depth – The deeper the liquid, the higher the pressure.
- Density – Denser liquids exert more pressure.
- Gravity – Greater gravitational pull increases pressure.
Formula: Pressure=Density×Gravity×Height
6.5 Explain that atmospheric pressure exerts pressure. What are its applications? Give at least three examples.
Atmospheric pressure is the force exerted by air around us.
Applications:
- Helps in breathing by allowing lungs to expand and contract.
- Used in vacuum packing to keep food fresh by removing air.
- Used in suction pumps and syringes to draw liquid.
Short Answer Questions
6.1 Why do heavy animals like an elephant have a large area of the foot?
Answer:
Heavy animals like elephants have large feet to reduce the pressure exerted on the ground. Pressure is given by: P=F/A
By increasing the area A, the pressure P on the ground decreases, helping them walk without sinking into soft ground.
Key Point: Large area = Reduced pressure.
6.2 Why do animals like deer who run fast have a small area of the foot?
Answer:
Fast-running animals like deer have small feet to increase pressure on the ground. This increases the grip and prevents slipping, allowing them to run quickly and maintain balance.
Key Point: Small area = Increased grip and agility.
6.3 Why is it painful to walk barefoot on pebbles?
Answer:
When walking barefoot on pebbles, the area of contact with the pebbles is very small. According to the pressure formula (P=F/A), a small area increases the pressure, causing pain.
Key Point: Small contact area = High pressure = Pain.
6.4 State Pascal’s law. Give an application of Pascal’s law.
Answer:
Pascal’s Law: Pressure applied to an enclosed fluid is transmitted equally in all directions throughout the fluid.
Application: Hydraulic brakes in vehicles use Pascal’s law to amplify force and stop vehicles efficiently.
Key Point: Equal pressure distribution in fluids is the core idea.
6.5 State what do you mean by elasticity of a solid.
Answer:
Elasticity is the property of a solid to return to its original shape and size after the removal of an external force causing deformation.
Key Point: Elasticity = Ability to regain original shape.
6.6 What is Hooke’s law? Does an object remain elastic beyond the elastic limit? Give a reason.
Answer:
Hooke’s Law: Within the elastic limit, the deformation of an object is directly proportional to the applied force: F∝x
Elasticity beyond the elastic limit: No, an object does not remain elastic beyond the elastic limit. Beyond this point, the object is permanently deformed and cannot return to its original shape.
Key Point: Elastic limit = Maximum limit of elasticity.
6.7 Distinguish between force and pressure.
Answer:
| Force | Pressure |
|---|---|
| It is a push or pull acting on an object. | It is the force applied per unit area. |
| Measured in newtons (N). | Measured in pascals (Pa). |
| Formula: F=ma | Formula: P=F/A |
Key Point: Force = Total impact; Pressure = Impact per unit area.
6.8 What is the relationship between liquid pressure and the depth of the liquid?
Answer:
Liquid pressure increases linearly with depth: P=ρgh
Where P is pressure, ρ is density, g is gravity, and h is depth.
Key Point: Greater depth = Greater liquid pressure.
6.9 What is the basic principle to measure the atmospheric pressure by a simple mercury barometer?
Answer:
The basic principle is the weight of the mercury column balances the atmospheric pressure. The height of the mercury column is directly proportional to the atmospheric pressure.
Key Point: Height of mercury = Atmospheric pressure.
6.10 State the basic principle used in the hydraulic brake system of automobiles.
Answer:
The hydraulic brake system is based on Pascal’s law, which states that pressure applied to an enclosed fluid is transmitted equally in all directions. This allows a small force on the brake pedal to generate a large braking force.
Key Point: Pascal’s law enables force amplification in braking systems.
