CBSE Sample Papers for Class 9 Science Set 2 with Solutions

Students must start practicing the questions from CBSE Sample Papers for Class 9 Science with Solutions Set 2 are designed as per the revised syllabus.

CBSE Sample Papers for Class 9 Science Set 2 with Solutions

Time : 3 Hrs.
Max. Marks : 80

General Instructions

• This question paper consists of 39 questions in 3 sections. Section A is Biology, Section B is Chemistry and Section C is Physics.
• All questions are compulsory. However, an internal choice is provided in some questions.
• A student is expected to attempt only one of these questions.

Section – A

Question 1.
Who discovered the free-living cell in pond water? [1]
(a) Virchow
(b) Robert Brown
(c) Purkinje
(d) Leeuwenhoek
Answer:
(d) Leeuwenhoek

Explanation:
Leeuwenhoek discovered the free-living cells in pond water for the first time.

Question 2.
The flexibility in plants is due to
(a) xylem
(b) collenchyma
(c) schlerenchyma
(d) parenchyma
Answer:
(b) collenchyma

Explanation:
The flexibility in plants is due to the presence of collenchyma. It allows bending of various parts of a plant like tendrils and stems of climbers without breaking.

Question 3.
Which are the correct statements related to prokaryotes? [1]
(i) Prokaryotes have an undefined nuclear region.
(iii) They contain membrane bound organelles.
(v) Most of them are unicellular organisms.
(a) (i), (iv) and (v)
(b) (ii), (iii) and (iv)
(c) (i), (ii) and (v)
(d) (ii), (iii) and (iv)
Answer:
(c) (i), (ii) and (v)

Explanation:
The statements (i),(ii) and (v) are correct as prokaryotes have an undefined nuclear region, contain a nucleoid instead of a true nucleus and most of them are unicellular.

Question 4.
Which of the following is a correct combination of connective tissue and its function? [1]
(a) Cartilage – connects muscles to bones
(b) Ligament – connects bones to bones
(c) Tendon – connects bones to nerves
(d) Blood – stores fat in the body
Answer:
(b) Ligament – connects bones to bones

Explanation:
Ligament connects bones to bones is the correct combination as ligaments join bones to other bones and help stabilise joints.

Question 5.
Which of the following is not a cell organelle? [1]
(a) Endoplasmic reticulum
(b) Golgi apparatus
(c) Plasma membrane
(d) Plastid
Answer:
(c) Plasma membrane

Explanation:
The plasma membrane is not considered as a cell organelle. It is a structure that surrounds the cell, regulating entry and exit of molecules.

Question 6.
Select the group in which all methods are used to improve soil fertility. [1]
(a) Crop rotation, use of pesticides, mixed cropping, irrigation, organic manure
(b) Crop rotation, organic manure, green manure, chemical fertilizers, mixed cropping
(c) Mixed cropping, crop rotation, overgrazing, use of chemical fertilizers, irrigation
(d) Overgrazing, use of chemical fertilizers, organic manure, crop rotation, deforestation
Answer:
(b) Crop rotation, organic manure, green manure, chemical fertilizers, mixed cropping

Explanation:
Crop rotation, organic manure, green manure, chemical fertilizers, mixed cropping belong to the same group as all of them are methods to improve soil fertility.

Question 7.
Which of the following is a biological method of pest control? [1]
(a) Use of chemical pesticides
(b) Crop rotation
(c) Use of natural enemies like ladybugs
(d) Using insecticide sprays
Answer:
(c) Use of natural enemies like ladybugs

Explanation:
Biological pest control uses natural enemies (like ladybugs) to control pests without harming the environment.

The following two questions consists of two statements Assertion (A) and Reason (R). Answer the questions by selecting the appropriate option given below.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.

Question 8.
Assertion (A) Fertilizer contains organic matter in large quantities. . [1]
Reason (R) Fertilizer is synthetic in nature that disrupts soil structure.
Answer:
(d) A is false, but R is true.

Explanation:
A can be corrected as fertilizers contains inorganic matter in large quantities.

Question 9.
Assertion (A) Two bones are connected to each other by a type of connective tissue. [1]
Reason (R) Tendons joins two bones together.
Answer:
(c) A is true but R is false.

Explanation:
R can be corrected as ligaments join two bones together.

Question 10.
Cytoplasm is called the living substance of the cell. Comment upon the statement with justification. [2]
Answer:
Cytoplasm is called the living substance of the cell because it is the site where many important life processes occur, such as respiration, protein synthesis, and growth. It contains enzymes and various cell organelles that carry out different functions necessary for the survival of the cell. Hence, cytoplasm plays an essential role in keeping the cell alive and active.

Question 11.
Attempt either A or B
A. Name the types of tissues responsible for the following functions in plants and explain how they help in these functions. [2]
(i) Transport of water
(ii) Transport of food
Answer:
(i) The tissue responsible for the transport of water in plants is xylem. It helps by conducting water and minerals from roots to other parts of the plant through hollow vessels.
(ii) The tissue responsible for the transport of food is phloem. It helps by transporting food made in the leaves to other parts of the plant through sieve tubes.

Or

B. Describe any four types of connective tissues in animals and mention one function of each.
Answer:
Different types of connective tissues in animals are: Bone provides support and protects organs.
Cartilage provides flexible support and reduces friction at joints.
Blood transports oxygen, nutrients, and waste products.
Ligaments connect bones to bones and stabilise joints.

Question 12.
A dairy farmer observed that cows fed with nutritious green fodder produced more milk than those fed with dry or poor-quality fodder. [2]
Explain why nutritious green fodder is important for milk production in animals.
Answer:
Nutritious green fodder is very important for milk production because it provides essential nutrients like proteins, carbohydrates, vitamins, and minerals that are necessary for the proper growth and health of dairy animals. These nutrients help in building and repairing body tissues and provide energy required for milk formation. Healthy and well-nourished animals produce more milk with better quality, which is beneficial for both farmers and consumers.

To obtain maximum marks students should also mention the name of essential nutrients.

Question 13.
Draw a diagram showing meiosis in a cell and explain why it is used in gamete formation? [3]
Answer:
Meiosis is important for the formation of gametes because it reduces the chromosome number to half
This helps in maintaining the correct number of chromosomes in the offspring after fertilization.

Question 14.
A beekeeper noticed that in one apiary, the honey production was consistently low despite having many bees. In another apiary, with fewer bees, the honey production was much higher. Upon investigation, he found that the first apiary had fewer flowering plants nearby, while the second had abundant flowering plants throughout the season. [3]
(a) Explain why honey production was low in the first apiary despite having more bees.
(b) Suggest two measures that the beekeeper can take to improve honey production in the first apiary.
Answer:
(a) Honey production was low in the first apiary because the bees did not have enough flowers to collect nectar from. Even if there are many bees, without sufficient flowering plants, they cannot gather enough nectar to produce honey.
(b) To improve honey production, the beekeeper should plant more flowering plants near the apiary to provide a good source of nectar. Also, providing proper shelter and maintaining the health of the bee colony will help increase honey production.

Question 15.
During an experiment, a student placed a plant cell in three different solutions: pure water, sugar solution of same concentration as the cell sap, and salt solution. The cell appeared swollen in pure water, normal in sugar solution and shrunken in salt solution. [4]
Attempt either subpart A or B
A. Which solution is hypertonic for the plant cell?
Answer:
The salt solution is hypertonic for the plant cell because it has higher concentration of solutes than the cell sap, causing water to move out and the cell to shrink.

Or
B. Which solution is hypotonic for the plant cell?
Answer:
Pure water is hypotonic for the plant cell because it has a lower concentration of solutes than the cell sap, causing water to move into the cell and making it swell.

C. What is plasmolysis, and in which solution did it occur?
Answer:
Plasmolysis is the process where the cell membrane pulls away from the cell wall due to loss of water. It occurs in the hypertonic solution.

D. The diagram given below shows a type of cell division. Identify the type of cell divison and explain why is it important?

Answer:
The given figure shows mitosis in cells. Mitosis is important because it helps in growth, repair, and replacement of old or damaged cells in the body.

Question 16.
Attemp either A or B
A. During a biology practical, Rahul prepared slides of onion root tip cells to observe cell division. He noticed that the cell division maintained the same number of chromosomes in the daughter cells as in the parent cell. [5]
(i) Identify the type of cell division seen by him and give reason.
(ii) How does this type of cell divison help in the growth of plants?
Answer:
(i) The type of cell division seen by Rahul is mitosis as in mitosis the chromosome number in the daughter cells remains the same.
(ii) Mitosis helps in the growth of plants by producing new cells that are genetically identical, which increases the number of cells and allows the plant to grow.

Or

B. A student was observing different types of cells under a microscope. A cell had well developed nuclear membrane, but B cell was deprived of nuclear membrane.
(i) Identify cell A and B.
(ii) Where is the genetic material located in cell A and B respectively.
Answer:
(i) Cell A is a eukaryotic cell because it has a well-developed nuclear membrane, and cell B is a prokaryotic cell as it lacks a nuclear membrane.
(ii) The genetic material in cell A is located inside the nucleus, whereas in cell B, it is present in the nucleoid region which is not enclosed by a nuclear membrane.

Section – B

Question 17.
A student during an experiment, heated solid ammonium chloride which directly changes to vapour and then gets deposited at the walls of funnel. Name the phenomenon taking place in the experiment. [1]

Option	First Process	Second process
(a)	Vaporisation	Deposition
(b)	Sublimation	Fusion
(c)	Sublimation	Deposition
(d)	Sublimation	Condensation

Answer:
(c)

Explanation:
In the given experiment, the phenomenon of sublimation and deposition takes place respectively.

Question 18.
Which of the following is not true about Bohr and Bury’s rule for electronic configuration, where n is the shell number? [1]
(a) The maximum number of electrons present in a shell is given by the formula 2n².
(b) The maximum number of electrons present in a shell is given by the formula 2n.
(c) The maximum number of electrons that can be accommodated in the orbit having n = 2 is 8.
(d) Electrons are not accommodated in a given shell, unless the inner shells are filled.
Answer:
(b) The maximum number of electrons present in a shell is given by the formula 2n.

Explanation:
Statement (b) is not true about Bohr and Bury’s rule for electronic configuration because the maximum number of electrons present in a shell is given by the formula 2n².

Question 19.
Which of the following statement does not support that water is a compound? [1]
I. Water is made up of two different elements (H and O) which chemically combined with one another in a fixed proportion.
II. Water has fixed boiling point (b.p.).
III. The constituents of water cannot be separated by simple physical methods.
IV. Distilled water and tap water have same taste and constituents.

(a) I and III
(b) II and III
(c) I, H, and IV
(d) Only IV
Answer:
(d) Only IV

Explanation:
Distilled water has pure H₂O molecules while tap water may contain others molecules also.

Question 20.
The phenomenon by which particles of a gas escape from the surface of a liquid into the air is called [1]
(a) condensation
(b) sublimation
(c) evaporation
(d) freezing
Answer:
(c) evaporation

Explanation:
Evaporation is the phenomenon by which particles of a gas escape from the surface of a liquid into the air.

Question 21.
The ratio by atomic mass of sulphur and oxygen in SO₂ will be [1]
(a) 1 : 4
(b) 1 : 2
(c) 1 : 1
(d) 2 : 1
Answer:
(c) 1 : 1

Explanation:
Atomic mass of sulphur = 32 u
Atomic mass of oxygen = 32 u
Ratio = 32: 32 = 1:1

Question 22.
Which one of the following is a group of elements having equal number of electrons, protons and neutrons? [1]
(a) N, Na, Al
(b) O, Na, Mg
(c) Mg, Si, Cl
(d) C, O, Mg
Answer:
(d) C, O, Mg

Explanation:
C, O and Mg is a group of elements having equal number of electrons, protons and neutrons.
C – Atomic number = No. of protons = 6
Mass number = (No. of protons + No. of neutrons)
12 – 6 = No. of neutrons
No. of neutrons = 6
No. of electrons = 6
Similarly, In ‘O’, the number of electrons, protons and neutrons are 8.
In ‘Mg’ the number of electrons, protons and neutrons are 12.

Question 23.
A student found that a metal X is forming an oxide with the formula – X₂O₃. What will be the formula of its chloride and sulphate? [1]
(a) X₂Cl₃ and X₂(SO₄)₃ respectively
(b) XCl and X₂(SO₄)₃ respectively
(c) XCl₃ and X(SO₄)₃ respectively
(d) XCl₃ and X₂(SO₄)₃ respectively
Answer:
(d) XCl₃ and X₂(SO₄)₃ respectively

Explanation:
A metal ‘X’ is forming an oxide = X₂O₃
So, the valency of X is +3.
Then, the formula of chloride of metal ‘X’ will be

Formula = XCl₃
Similarly,
The formula of sulphate of metal ‘X’ will be

Formula = X₂(SO₄)₃

The following question consists of two statements -Assertion (A) and Reason (R). Answer the question by selecting the appropriate option given below.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.

Question 24.
Assertion (A) Brass is an alloy of mixture of zinc (30%) and tin (70%). [1]
Reason (R) Alloys are mixture of two or more metals or a metal and a non-metal and cannot be separated into their components by physical methods.
Answer:
(d) A is false, but R is true.

Explanation:
(A) is false, but (R) is true. Assertion can be corrected as brass is an alloy of mixture of zinc (30%) and copper (70%).

Question 25.
Given below is electron distribution of an unknown element.

Based on this information, answer the following questions.
(a) Based on the electron configuration of element X (2, 8, 5), identify a non-metal that exists as a tetra-atomic molecule. Justify your answer.
(b) What is atomicity? Give the atomicity of the non-metal identified above and support it with an example.
Answer:
(a) The given element X has the electron distribution 2, 8, 5, indicating it has 5 valence electrons. A non-metal with a similar configuration is phosphorus (P).

• Phosphorus is a tetra-atomic molecule in its elemental form (P₄).
• Phosphorus atoms bond together to form (P₄) molecules for stability.

(b) Atomicity is the number of atoms present in one molecule of an element, e.g. phosphorus (P₄) has an atomicity of 4.

Phosphorus has five electrons in its outermost shell. This means that the valency of phosphorus is 3.

Question 26.
Attempt either A or B. [3]
A. Give one property of each of the following.
(a) Elements
(b) Metals
(c) Non-metals
Answer:
(a) Elements are the basic form of matter that can not be broken down into simpler substances by chemical methods.
(b) Metals generally have a silvery-grey or golden yellow colours.
(c) Non-metals are generally not lustrous, sonorous or malleable.

Or

B. Answer the following questions based on the above given diagram.
(a) Name the type of mixture that shows this property and give one everyday example.
(b) Why copper sulphate solution will not show this property whereas milk will show?
(c) Which property is shown in the given diagram?
Answer:
(a) This property is exhibited by colloidal mixtures. Fog and milk are everyday example of colloidal mixtures.
(b) Copper sulphate solution is a true solution with particle size less than 1 nm, so it does not scatter light and shows no Tyndall effect. Whereas, milk is a colloidal solution and thus, the particles are big enough to scatter light. Therefore, it exhibits Tyndall effect.
(c) The given diagram shows the property of Tyndall effect.

Question 27.
State reasons for the following. [3]
(a) A gas exerts pressure on the walls of the container.
(b) Our palm feels cold when we put some acetone or petrol or perfume on it.
(c) Ice at 273 K is more effective in cooling than water at the same temperature.
Answer:
(a) Due to high kinetic energy possessed by the gas particles, they randomly move at a high speed within the container. Due to this random movement, the particles hit each other as well as  the walls of the container. The force by which these particles strike the container exerts a pressure on its walls.
(b) Acetone, petrol and perfume are volatile liquids which evaporate readily. When these liquids are kept on palm their particles gain energy from the palm or surrounding and evaporate, thus causing the palm to cool.
(c) When ice at 273 K melts to form water at 273 K, it absorbs heat energy equal to the latent heat of fusion from the surroundings. Thus, ice at 273 K has less heat energy than water at 273 K and hence ice is more effective in cooling than water at the same temperature.

Question 28.
Neils Bohr improved upon Rutherford’s atomic model. He proposed that electrons revolve around the nucleus in fixed circular paths known as energy levels or shells. These shells are represented as K, L, and each shell has a fixed energy. While in a particular orbit, an electron does not radiate energy, ensuring the stability of the atom. The energy levels in an atom are shown in the table given below. [4]

(Principal quantum number)	Shell number
1	K
2	L
3	M

A. A newly discovered element has its outermost electron in the shell where n = 5. What is the name of this shell and how many electrons can it theoretically hold?
(a) O-shell, 72 electrons
(b) P-shell, 100 electrons
(c) O-shell, 50 electrons
Justify your answer.
Answer:
(c) O-shell, 50 electrons

Explanation:
According to Bohr’s model, shells are named in alphabetical order starting from K(n = 1), L(n = 2), M(n = 3), N(n = 4), and so on.
n = 5 → O-shell
The maximum number of electrons is given by 2n² = 2 × (5)² = 2 × 25 = 50

B. What is meant by energy level in Bohr’s model? How are these represented?
Answer:
Energy level is the fixed path or shell in which an electron revolves around the nucleus.
They are represented as K, L, M, N… or n = 1, 2, 3, 4…

Or

How did Bohr’s model explain the stability of the atom?
Answer:
According to Bohr, since electrons move in stable orbits without losing energy, so they do not spiral into the nucleus, hence the atom remains stable.

C. Which of the following statements about Bohr’s model of the atom is true and why?
(a) Electrons revolve randomly around the nucleus.
(b) Electrons radiate energy while moving in fixed orbits.
(c) Electrons revolve in fixed orbits with quantised energy levels.
(d) The nucleus contains electrons and protons mixed together.
Answer:
(c) Electrons revolve in fixed orbits with quantised energy levels.

Explanation:
Bohr proposed that electrons move in specific, fixed paths around the nucleus, and each orbit has a definite energy level, preventing loss of energy during motion.

Question 29.
A. Hydrogen gas reacts with oxygen gas to form water shown in the following reaction.
2H₂ + O₂ → 2H₂O
This experiment was conducted in a closed container. Answer the following questions.
(a) Which law of chemical combination is illustrated in this reaction? State the law.
(b) Calculate the total mass of reactants and the total mass of the product. Does this support your answer in part (a)?
(c) What will be the mass ratio of hydrogen to oxygen in water? Which law does this constant ratio support?
(d) Calculate the number of moles of hydrogen and oxygen gases used in the reaction.
(e) Give one more example of a reaction that follows the law of constant proportion and name the compound formed.
Answer:
(a) This reaction illustrates the law of conservation of mass.
“Mass can neither be created nor destroyed in a chemical reaction. The total mass of the products is equal to the total mass of the reactants.

(b) Mass of reactants = 4 g (H₂) + 32 g (O₂) = 36 g Mass of product = 36 g (H20)
Since the mass of reactants is equal to the mass of the product, this supports the law of conservation of mass.

(c) In water, hydrogen and oxygen combine in the ratio
Hydrogen: Oxygen = 4g : 32g = 1: 8.
This supports the law of constant proportion, which states that a chemical compound always contains the same elements in a fixed ratio by mass.

(d) Molar mass of H₂ =2 g/mol
Moles of H₂ = 4g + 2 g/mol = 2 mol
Molar mass of O₂ = 32 g/mol
Moles of O₂ = 32g + 32 g/mol = 1 mol

(e) The compound formed is carbon dioxide (CO₂).
Carbon and oxygen always combine in a mass ratio of 12: 32 = 3: 8, which is constant.
C + O₂ → CO₂

Or

B. (a) Define Dalton’s atomic theory.
(b) According to Dalton, what are atoms ? Are they divisible or indivisible.
(c) Give atleast three postulates of Dalton’s atomic theory.
(d) Name two postulates of Dalton’s theory that have been proved incorrect in modem science.
(e) How did Dalton’s atomic theory contribute to the understanding of chemical reactions?
Answer:
(a) Dalton’s atomic theory is a scientific theory that states all matter is made up of tiny indivisible particles called atoms, which takes part in chemical reactions.

(b) According to Dalton, atoms are indivisible and indestructible particles of matter. They cannot be created or broken down by chemical means.

(c) Three postulates of Dalton’s atomic theory are
1. all matter is made of indivisible atoms.
2. atoms of a given element are identical in mass and properties.
3. atoms combine in simple whole-number ratios to form compounds.

(d) Two postulates now proved incorrect are
1. Atoms are indivisible Modem science shows atoms can be divided into protons, neutrons, and electrons.
2. Atoms of an element are identical in mass Isotopes of the same element have different masses.

(e) Dalton’s theory helped understand chemical reactions as rearrangements of atoms, where no atom is created or destroyed, only recombined.

Section – C

Question 30.
The graph shows the velocity versus time for two objects, A and B. [1]

I. The object represented by line A has a greater acceleration than the object represented by line B.
II. The object represented by line B has a greater acceleration than the object represented by line A.
III. Both objects A and B have the same acceleration.

Which of the following options is correct in that lists ?
(a) Only I
(b) Only II
(c) Only II
(d) I and II
Answer:
(a) Only I

Explanation:
From the velocity-time graph, we can determine that the slope of the graph represents the acceleration of the objects. Object A has a steeper slope, indicating a greater acceleration compared to object B, which has a gentler slope. Therefore, the correct answer is (a)
I only, as object A has a greater acceleration than object B.

Question 31.
Which of the following figures represent uniform motion of a moving objects correctly?

Answer:
(a) Uniform motion of moving object is as given below.

The following questions consists of two statements — Assertion (A) and Reason (R). Answer the questions by selecting the appropriate option given below.
(a) Both (A) and (R) are true and (R) is the correct explanation of (A).
(b) Both (A) and (R) are true, but (R) is not the correct explanation of (A).
(c) (A) is true, but (R) is false.
(d) (A) is false, but (R) is true.

Question 32.
Assertion (A) The gravitational force varies on changing the mass of the object.
Reason (R) The gravitational force between any two objects is directly proportional to the product of their masses and inversely proportional to the square of distance between them.
Answer:
(a) Both (A) and (R) are true and (R) is the correct explanation of (A).

Explanation:
According to Newton’s universal law of gravitation,
Gravitational force is given by
F = \(\frac{G m_1 m_2}{r^2}\)
F ∝ m₁m₂

If the mass of the object changes, F will also vary.

Question 33.
A hospital uses ultrasound waves of frequency 2.0 MHz for detecting the growth of a tumour inside the human body. The speed of sound in human tissues is approximately 1.5 x 103 m/s. [2]
(a) Calculate the wavelength of these waves in the body.
(b) The tumour is 4.0 cm below the skin surface, calculate the time taken for the ultrasound pulse to return to the detector.
(c) Explain, why ultrasound is preferred over audible sound for such medical imaging?
Answer:
(a) Wavelength, λ = \(=\frac{v}{f}=\frac{1.5 \times 10^3}{2.0 \times 10^6}\)
= 7.5 × 10⁴ m = 0.75 mm

(b) Time for pulse to return
The total distance travelled
= 2 × 40 cm = 8.0 cm = 0.08 m
t = \(\frac{\text { Distance }}{\text { Speed }}=\frac{0.08}{1.5 \times 10^3}\) ≈ 5.33 × 10⁵ s = 53.3 ps

(c) Ultrasound has very small wavelengths, allowing it to detect tiny structures and irregularities in tissues, which audible sound cannot resolve.

Question 34.
Attempt either A or B
A. The image shows a spring and a ball with two hands pressing the ball. [2]

(a) Explain the type of force involved when the ball is pressed between the hands. What happens to the shape of the ball during this action?
(b) How does the force exerted by the spring differ from the force applied by the hands on the ball? Describe the nature of forces in both cases.
Answer:
(a) The force applied when the ball is pressed is compressive force. This force deforms the ball, causing it to change shape, usually by compressing or squishing it. [1]
(b) The force by the spring is elastic force, which works to restore the spring’s shape when compressed. The force by the hands is a . mechanical compressive force that squeezes the ball, causing deformation without any restoring action.

Or
B. A wooden block is placed on a table with two forces X and Y acting on it in opposite directions, as shown in the figure.

(a) If the magnitudes of the two forces are equal, what will be the net force acting on the block? Explain your answer.
(b) What will happen to the motion of the block, if one force is greater than the other? Justify your answer with reference to Newton’s laws of motion.
Answer:
(a) If the magnitudes of the two forces are equal, the net force on the block will be zero. This is because the forces cancel each other out, resulting in no motion. [1]
(b) If one force is greater than the other, the block will move in the direction of the greater force. This is explained by Newton’s second law of motion, which states that an object will accelerate in the direction of the net force applied to it.

Question 35.
In a large hail, a concave sound board is placed behind the speaker as shown in the figure.

(a) If the speaker produces sound waves with a speed of 343 m/s and frequency 686 Hz, calculate the wavelength.
(b) A student claims that, if the sound board were flat instead of concave, the sound would spread more evenly. Is the student correct? Justify your answer using the concept of reflection of sound waves.
Answer:
(a) λ = \(\frac{v}{f}=\frac{343}{686}\) = 0.50 m
So, the wavelength of the sound in air is 0.50 m.

(b) No, the student is not correct in the sense of improving audibility at a distance.
A flat board reflects sound but does not focus it reflected waves tend to remain as many divergent rays, so sound energy is not concentrated toward the audience.
A concave board concentrates/refocuses the sound (acts like a reflector), giving stronger sound at selected audience regions.

Question 36.
Two spheres of mases 40 kg and 60 kg are placed 0.5 m apart (measured between their centres).
Take, G = 6.67 x 10^-11 Nm² /kg². [3]

(a) Calculate the gravitational force between them. If the distance between them is doubled, find the new gravitational force.
(b) State the ratio of the initial force to the new force and explain the reason.
Answer:
Given,
mass of sphere 1, m₁ = 40 kg
mass of sphere 2, m₂ = 60 kg
Separate by the distance = 0.5 m

The force becomes one-fourth when the distance is doubled, due to the inverse square law.

Students often forget to square the distance when appLying the Law of gravitation.

Question 37.
Two objects A and B, have equal volumes but different masses. Object A is made of wood and object B is made of metal. Both are initially at rest on a frictionless horizontal surface. [3]
(a) Explain with reasons, which object has greater inertia and why?
(b) A constant horizontal force is applied to each object separately. Compare their accelerations and explain, how the difference in inertia affects their motion?
Answer:
(a) Inertia is the tendency of an object to resist any change in its state of motion. It depends directly on the mass of the object. Since, both objects A (wood) and B (metal) have equal volumes, but metal is denser than wood; object B will have greater mass. Therefore, object B has greater inertia because inertia increases with mass.

(b) According to Newton’s second law, F = m × a
where, F is the applied force, m is the mass and a is the acceleration.
Rearranging, a = \(\frac {F}{m}\)
Since, the for,ce F is the same for both objects but object B has a greater mass m, the acceleration of object B will be less than that of object A.
This means object A (wood) will accelerate more because it has less inertia (less mass). Object B (metal) will accelerate less due to its greater inertia resisting the change in motion. [154]

To get maximum marks, clearly explain Newton’s
second law a = \(\frac {F}{m}\) and state that the object with smaller mass accelerates more due to less inertia.

Question 38.
The distance travelled by a moving body is the actual length of the path covered by it, irrespective of the direction in which the body travels. It is a scalar quantity. Its SI unit is metre. [4]
e.g. Consider the motion of an object moving along a straight path. Speed of an object is defined as the distance travelled by it per unit time.
Speed of an object (v) = \(\frac{\text { Distance }(s)}{\text { Time }(t)}\)
Speed is a scalar quantity. The SI unit of speed is metre per second (m/s). The distance travelled by an object is either positive or zero, so the speed may be positive or zero but never negative. Distance travelled by a train and time taken by it is shown in the following table.

Time	Distance (in km)
10:00 am	0
10:30 am	25
10:40 am	30
11:00 am	40
11:15 am	42
11:30 am	50

A. Draw the graph which shows distance-time relationship. At what time, the train is travelling at its highest speed.
Answer:

We know that, speed = slope of distance-time graph. The greater slope and the greater speed. From the graph, it is clear that the slope of distance-time graph is maximum between 10:00 am 10:30 am, so the train is travelling at its highest speed during this interval of time.

B. At what distance does the train slows down?
Answer:
The part CD of the graph has minimum slope, so the train had minimum speed between 11:00 am and 11:15 am. Thus, the train had slowed down between 40 km and 42 km.

Attempt either C or D
C. What is the average speed of the train?
Answer:
Average speed = \(\frac{\text { Total distance travelled }}{\text { Total time taken }}\)
From the given table, total distance travelled = 50 km
Total time taken 10:00 am to 11:30 am
= 1 h 30 min = 1\(\frac {1}{2}\) h = \(\frac {3}{2}\) h
Now, average speed = \(\frac{50}{\frac{3}{2}}=\frac{100}{3}\) = 33.33 km/h

Or

D. Calculate the speed of the train between 10 : 30 am to 10 : 40 am.
Answer:
Distance travelled between 10:30 am to 10:40 am,
D = 30 – 25 = 5 km
t = 10 min = \(\frac {1}{2}\) h
Speed between 10: 30 am to 10: 40 am
= \(\frac{\text { Distance travelled }}{\text { Time }}=\frac{5}{\frac{1}{6}}\) = 30 km/h

Question 39.
Attempt either A or B. [5]
A. (a) State the law of conservation of energy. Give an example in which we observe a continuous change of one form of energy into another and vice-versa.
(b) Calculate the amount of work required to stop a car of 1000 kg moving with a speed of 72 km/h. An engine pulls train 1 km over a level track.
(c) Calculate the work done by the train given that the frictional resistance is 5 × 10⁵ N.
Answer:
(a) The law of conservation of energy can only be converted from one form to another, it can neither be created nor destroyed. The total energy before and after the transformation remains the same, e.g. A swinging pendulum, continuously converts energy. At its highest point, it has maximum potential and minimum kinetic energy. As, if swings downward, potential energy converts to kinetic, energy reversing as it rises.

(b) Given, m = 1000 kg
u = 72 km/h
= 72 × \(\frac{5}{18}\) = 20 m/s
v = 0

Initial kinetic energy = \(\frac{1}{2}\) mv
= \(\frac{1}{2}\) × 1000 × (20)² = 200000J
= 2 × 10⁵ J
Final KE = 0
Work done = Change in KE = 2 × 10⁵ J

(c) Frictional resistance, F = 5 × 10⁵ N
Distance through which the train moves, s = 1km = 1000 m
Work done by the frictional force i.e.
W = Fs = 5 × 10⁵ × 1000 = 5 × 10⁸ J
(F and s are in opposite directions)
Obviously, work done by the train is 5 × 10⁸ J.

Or

B. A 5 kg ball is thrown upward with a speed of 10 m/s attains a height of 10 m.
(a) Find the potential energy when it reaches the highest point.
(b) Calculate the maximum potential energy, when it reaches the ground.
(c) A body is thrown up with kinetic energy of 10 J. If it attains a maximum height of 5 m, find the mass of the body.
Answer:
(a) Here, mass of the ball, m = 5 kg
Height of the ball, h = 10 m
Potential energy of the ball, at highest point
E_P = mgh = 5 × 9.8 × 10 = 490 J

(b) When the ball reaches the ground, its potential energy becomes zero as it is entirely converted into its kinetic energy (EK),
⇒ E_K = 490 J.

(c) Kinetic energy of the body, E_K = 10 J
Maximum height attained by the body, h = 5 m
When the body attains maximum height, its entire kinetic energy is converted into its potential energy, i.e. E_P = E_K
mgh = 10 => m = \(\frac{10}{g h}\)
⇒ m = \(\frac{10}{10 \times 5}\)
⇒ m = 0.2 kg