CBSE Sample Papers for Class 9 Science Set 7 with Solutions

Students must start practicing the questions from CBSE Sample Papers for Class 9 Science with Solutions Set 7 are designed as per the revised syllabus.

CBSE Sample Papers for Class 9 Science Set 7 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.
Select the group in which all the tissues are connective tissues. [1]
(a) Bone, cartilage, blood, tendon, ligament
(b) Muscle, bone, cartilage, blood, epithelial
(c) Ligament, tendon, skeletal muscle, cartilage, blood
(d) Cartilage, epithelial, blood, muscle, ligament
Answer:
(a) Bone, cartilage, blood, tendon, ligament

Explanation:
Bone, cartilage, blood, tendon, ligament because all are connective tissues that connect, support and bind other tissues and organs in the body.

Question 2.
Which of the following options indicates the substances that can pass freely through the plasma membrane by diffusion? [1]
(a) Glucose and proteins
(b) Oxygen and carbon dioxide
(c) Starch and DNA
(d) Amino acids and enzymes
Answer:
(b) Oxygen and carbon dioxide

Explanation:
Oxygen and carbon dioxide can pass freely through the plasma membrane by diffusion because plasma membrane is selectively permeable and allows only certain substances to pass through like oxygen (O₂) and carbon dioxide (CO₂).

Question 3.
Which of the following is not a method adopted for irrigation of crops? [1]
(a) Wells
(b) Canals
(c) Rainfall
(d) Tanks
Answer:
(c) Rainfall

Explanation:
Rainfall is the natural source of water, not an irrigation system.

Question 4.
In a certain cell, the plasma membrane controls the movement of substances in and out of the cell. Which of the following statements is correct about the plasma membrane? [1]
(a) It is made up only of proteins.
(b) It is a rigid structure that does not allow any substances to pass.
(c) It is selectively permeable, allowing only certain substances to enter or leave the cell.
(d) It is present only in animal cells, not in plant cells.
Answer:
(c) It is selectively permeable, allowing only certain substances to enter or leave the cell.

Explanation:
The plasma membrane is a thin, flexible layer that surrounds the cell. This structure allows the membrane to control the movement of substances in and out of the cell by allowing some substances to pass, while blocking others. This property is called selective permeability.

Question 5.
Which of the following substances is transported by xylem in plants? [1]
(a) Water and minerals
(b) Food (glucose)
(c) Hormones only
(d) Oxygen
Answer:
(a) Water and minerals

Explanation:
Xylem transport water and dissolved minerals from roots to the other parts of the plants.

Question 6.
Which of the following statements about bone are correct? [1]
(i) Bone matrix is hard and non-flexible, containing calcium and phosphorus compounds.
(ii) Bone provides a rigid framework that supports the body.
(iii) Bone connects muscles to each other.
(iv) Bone anchors muscles and protects internal organs.

(a) i, ii and iv only
(b) i and iii only
(c) ii, iii and iv only
(d) i, ii, iii and iv
Answer:
(a) i, ii and iv only

Explanation:
Bone matrix is hard due to calcium and phosphorus compounds, providing rigidity, Bones form a rigid framework that supports the body and anchor muscles.

Question 7.
Sclerenchyma cells differ from collenchyma cells because they [1]
(a) have thick, lignified walls and are dead at maturity.
(b) are flexible and provide elasticity to the plant.
(c) store food and have thin cell walls.
(d) conduct photosynthesis actively.
Answer:
(a) have thick, lignified walls and are dead at maturity.

Explanation:
Sclerenchyma cells have thick, hard and lignified cell walls that provide mechanical support and strength to the plant whereas collenchyma cells have unevenly thickened, flexible cell walls and are alive at maturity.

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) Columnar epithelium is specialised for absorption and secretion. [1]
Reason (R) Cells of columnar epithelium are thin and flat, providing a large surface area for diffusion.
Answer:
(c) A is true, but R is false.

Explanation:
R can be corrected as
Columnar epithelium consists of tall, pillar-like cells. It is specialised for absorption and secretion.

Question 9.
Assertion (A) Xylem is responsible for the conduction of water arid minerals from roots to other parts of the plant. [1]
Reason (R) Food prepared by leaves is also transported through xylem.
Answer:
(c) A is true, but R is false.

Explanation:
It can be corrected as
The transport of food materials such as sugars, produced during photosynthesis in the leaves, is performed by the phloem.

Question 10.
In a composite fish culture system, a combination of five or six fish species is used in a single fishpond.
Comment upon the statement with justification. [2]
Answer:
A combination of five or six fish species is used in a single fishpond. These species are selected so that they do not compete for food among them having different types of food habits. As a result, the. food available in all the parts of the pond is used. As some of fishes are surface feeders, some feed in the middle zone of the pond, while others are bottom and weed feeders.

Question 11.
Attempt either A or B.
A. Describe the function of the following cell organelles and mention the number of membranes surrounding them. [2]
Answer:
The functions of the given cell organelles are
(i) Mitochondria Mitochondria have two membrane coverings. The energy required for various chemical activities needed for life is released by mitochondria in the form of ATP (Adenosine triphosphate) molecules.
ATP is known as the energy currency of the cell. The body uses energy stored in ATP for making new chemical compounds and for mechanical work.

(ii) Chloroplast Chloroplasts have two membrane coverings and contain the pigment called chlorophyll. They are important for photosynthesis in plants.

Or

B. Explain the process of osmosis and the movement of water in hypotonic.
Answer:
Osmosis is the net diffusion of water across a selectively permeable membrane toward a higher solute concentration. When a cell is placed in a hypotonic solution, water enters the cell by the process of osmosis.

Question 12.
What is the role of ligaments in the body? How are tendons different from ligaments? [2]
Answer:
Ligaments are tough, elastic connective tissues that connect bones to other bones at joints. They provide stability to joints by holding the bones together and preventing excessive movements that could cause injury. Tendons connect muscles to bones whereas Ligaments connect bones to bones and provide stability to joints.

Question 13.
Draw and label the structure of a striated muscle fibre. Explain how striated muscles help in voluntary movements. [3]
Answer:
A striated muscle fibre is long, cylindrical and has many nuclei present on its surface. They are attached to the bones and help in voluntary movements of the body. These muscles contract and relax when controlled by our will. For example, when you decide to lift your hand, the striated muscles in your arm contract, causing the movement.

Question 14.
Abiology student examined two types of connective tissues under a microscope – one with a hard matrix and another with a fluid matrix. [3]
(i) Name both types of connective tissues. Write one function of each.
(ii) If another tissue with the solid matrix is observed, which tissue is this and where it can be found.
Answer:
(i) Hard matrix tissue are bone and its function is to provide shape, support and protection to the body. Fluid matrix tissue are blood and its function is to transports oxygen, nutrients, hormones and waste products.
(ii) The tissue of solid matrix is cartilage, which is compsed of proteins and sugars. Cartilage smoothens the bone surface at joints and is present in the nose, ear, trachea and larynx.

To obtain maximum marks, also mention the function and composition of cartilage.

Question 15.
The diagram below represents an animal cell. Help Priya understand the roles of different organelles by answering the following questions. [4]
Attempt either subpart A or B.
A. Which organelle in the animal cell helps in removing waste materials and worn-out cell parts? Describe its structure and give one function.
Answer:
Lysosome helps in removing waste materials and worn-out cell parts. They are small, spherical sac-like structures containing digestive enzymes. Thus, they are known as suicidal bag of the cell.

Or

B. Which organelle is responsible for packaging proteins and transporting them within the cell? Name one more function of this organelle.
Answer:
Golgi body is responsible for packaging proteins and transporting them within the cell.

C. Name the organelle that helps in energy production animal cells. Which molecule is produced during this process?
Answer:
Mitochondria helps in energy production animal cells, as it produces ATP (Adenosine Triphosphate), which is the energy source of the cell.

D. The figure shows parts labelled A, B, C, D and E. Identify the part where cell membranes are formed and write its function.

Answer:
The part E is the endoplasmic reticulum where cell membranes are formed. It helps in the synthesis and transport of proteins and lipids.

Question 16.
Attempt either A or B.
A. Ramesh has a small piece of land where he wants to grow wheat. [5]
(i) Based on your knowledge of cropping seasons, should he sow the seeds in July or November? Justify your answer.
(ii) The soil on his farm is nutrient-deficient, leading to low wheat production. Suggest two ways to restore soil fertility and explain how each method helps improve crop yield.
Answer:
(i) Ramesh should sow the wheat seeds in November. Wheat is a rabi crop, which means it is grown in the winter season. Sowing in November allows the crop to grow during the cool months, which is ideal for wheat.
(ii) By using organic manure as they also improve soil texture and water-holding capacity, which helps in better growth of wheat and by using chemical fertilisers that ensure that crops get the required nutrients for healthy growth, leading to higher wheat production.

Or

B. Ravi wanted to improve the yield of tomato plants in two different plots. He used high-yielding tomato seeds in Plot A and normal seeds in Plot B. He also ensured regular irrigation and use of bio-fertilisers in Plot A only.
(i) What difference will he observe in the yield between the two plots? Give a reason based on agricultural practices.
(ii) Write any three methods by which farmers improve food production.
Answer:
(i) Plot A will produce a higher yield of tomato plants because high-yielding variety seeds have been developed to produce more fruits per plant. Along with proper irrigation and use of bio-fertilisers, these factors help plants grow better and produce more tomatoes.

(ii) Three methods by which farmers improve food production are
(a) use of High Yielding Variety (HYV) seeds
(b) use of fertilisers and pesticides to provide nutrients and protect crops from pests
(c) providing proper irrigation to ensure adequate water supply for plants.

Section – B

Question 17.
Four statements about subatomic particles and atomic models are listed. [1]
I. Electrons are negatively charged and were discovered by Rutherford.
II. Protons are heavier than neutrons and are positively charged.
III. Rutherford’s model could not explain the stability of atoms.
IV. The mass of an atom is mainly concentrated in the nucleus.

Which statements are correct?
(a) I and II
(b) I and III
(c) III and IV
(d) II and IV
Answer:
(c) III and IV

Explanation:
Statement III is correct as Rutherford’s model couldn’t explain why electrons, moving around the nucleus, don’t lose energy and spiral in. Statement IV is also correct as the mass of an atom is concentrated in the nucleus due to protons and neutrons.

Question 18.
Matter may be classified as elements, compounds or mixtures. Which of the following lists includes only mixtures? [1]
(a) Sea water, milk, air
(b) Copper, gasoline, bread
(c) Paint, blood, mercury
(d) Dry ice, alcohol, brass
Answer:
(a) Among the following options, list given in option (a), i.e. sea water, milk and air includes only mixture.

Question 19.
Which of the following pair of molecules of compound have the same atomicity? [1]
(a) C₆H₁₂O₆ and (NH₄)₃ PO₄
(b) NH₃ and CaCl₂
(c) K₂MnO₄ and H₃BO₃
(d) NH₄OH and CH₃COOH
Answer:
(c) K₂MnO₄ and H₃BO₃

Explanation:
Among the given pair of molecules of compound, K₂MnO₄ and H₃BO₃ have same atomicity, i.e., 7.
While others have C₆H₁₂O₆ = 24
(NH₄)₃ PO₄ = 20
NH₃ = 4
CaCl₂ = 3
NH₄OH = 7
CH₃COOH = 8

Question 20.
A small amount of solid is taken in two separate china dishes ‘A’ and ‘B’. Dish ‘A’ is gently heated, and dish ‘B’ is left at room temperature. It is observed that the solid in dish A’ disappears completely without melting, while no change occurs in dish ‘B’. What inference can be drawn from this? [1]
(a) The solid in dish ‘A melts quickly on heating, while the one in ‘B’ requires more heat.
(b) The solid in dish ‘A is volatile and melts easily, while the one in ‘S’ is non-volatile.
(c) The solid in dish A’ undergoes sublimation, while the solid in dish ‘S’ does not.
(d) Both solids are the same and will eventually melt or evaporate.
Answer:
(c) The solid in dish A’ undergoes sublimation, while the solid in dish ‘S’ does not.

Explanation:
The solid in dish A’ changes directly from solid to gas on heating, which is characteristic of sublimation. No change in dish ‘B’ indicates the substance does not undergo sublimation at room temperature.

Sublimation is a process in which a solid substance directly converts into its gaseous form without passing through the liquid phase.

Question 21.
What is the molecular mass of methanol (CH₃OH)? [1]
(a) 58 u
(b) 32 u
(c) 40 u
(d) 48 u
Answer:
(b) The molecular mass of methanol (CH₃OH)
= (Atomic mass of carbon × 1) + (Atomic mass of hydrogen × 3) + (Atomic mass of oxygen × 1) + (Atomic mass of hydrogen xl)
= (12 u × 1) + (1 u × 3) +(16 u × 1) +(1 u × 1)
=(12 + 3 + 16 + 1) u
= 32 u

Question 22.
Two elements X and Y form a compound in which the ratio of their masses is 1:1 and the atomic mass of Y is half of the atomic mass of X. What is the formula of the compound? [1]
(a) XY
(b) XY₂
(C) X₂Y
(d) X₂Y₂
Answer:
(b) Let the atomic mass of ‘X’ = x
Therefore, the atomic mass of ‘Y’ = \(\frac {x}{2}\)
Since, the compound has a 1 :1 mass ratio of X and Y, we can assume that the mass of X is equal to the mass of Y in the compound, i.e., m grams.
Now, using the atomic masses, we can set up the following equation
xm + \(\frac {x}{2}\)m = 2m
2xm + xm = 4m
3xm = 4 m
⇒ x = \(\frac {4}{3}\)
So, the atomic mass of ‘X’ = \(\frac {4}{3}\) and atomic mass of ‘Y’ = \(\frac {4}{6}\)
On simplifying the ratio we get X: Y = 2 :1
Hence, the formula of the compound will be XY₂.

Question 23.
The mass of an element is concentrated in the nucleus as explained by Rutherford. Which element will have mass number 7? [1]

Element	Proton	Neutron	Electron
(a)	1	1	1
(b)	3	4	3
(c)	4	3	4
(d)	2	3	2

Answer:
(b) Given, no. of protons = 3
No. of neutrons = 4
No. of electrons = 3
Mass number = No. of protons + no. of neutrons = 3 + 4 = 7

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) The rate of diffusion of liquids is lower than that of solids. [1]
Reason (R) In the liquid state, particles move freely and have greater space between each other as compared to particles in the solid state.
Answer:
(d) A is false, but R is true.

Explanation:
(A) can be corrected as the rate of diffusion of liquids is higher than that of solids.

Question 25.
Given below is electron distribution of an unknown element. [2]
(a) The given element X has its valency equal to +3, what will be its formula with carbonate ions?
Answer:

(b) Calculate the formula unit mass of NaHCO₃.
[Atomic mass of Na = 23 u, H = 1 u, C = 12 u, O = 16 u]
Answer:
NaHCO₃ = (Atomic mass of Na) + (Atomic mass of H) + (Atomic mass of C) + (3 x Atomic mass of O)
= (23 + 1 + 12 + 3 × 16) u
= 84 u

Question 26.
Attempt either A or B.
A. Find the ratio by mass of the combining elements in the following compounds
(a) CaCO₃
(b) MgCl₂
(c) H₂SO₄
Answer:
(a) The ratio of the mass of CaCO₃
Ca : C : O × 3
40 : 12 : (16 × 3)
40 : 12 : 48
Hence, the ratio of the mass of CaCO₃ is 10 : 3 : 12.

(b) The ratio of the mass of MgCl₂
Mg : Cl × 2
24 : 35.5 × 2
24 : 71
Hence, the ratio of the mass of MgCl₂ is 24: 71.

(c) The ratio of the mass of H₂SO₄
H × 2 : S : O × 4
1 × 2 : 32 : 64
2 : 32 : 64
1 : 16 : 32
Hence, the ratio of the mass of H₂SO₄ is 1:16: 32 [1]

Or

B. The structure of a phosphoric acid molecule is given below.

Two atoms are joined through covalent bonds represented by dash (—). Covalent bonds held the combining atoms together. The number of covalent bonds formed by an atom signifies the combining capacity of an atom.
(a) What is the valency of phosphorus atoms in phosphoric acid?
(b) The formula of phosphoric acid is written as H_xP_yO_z. Write the value of x, y, and z in increasing order.
(c) Calculate the mass percentage of phosphorus in a phosphoric acid molecule if the average atomic mass of phosphorus is 31 u.
Answer:
(a) The valency of phosphorus atom in phosphoric acid is + 5.
(b) The formula of phosphoric acid is written as H_xP_yO₄, then the value of x,y and z (3, 1, 4) in increasing order is y < x < z, 1 < 3 < 4.

Don’t make mistake of arranging the elements if you have not calculated the correct valencies first

(c) Given, the average atomic mass of phosphorus is 31 u.
Molecular mass of phosphoric acid (H₃PO₄) = (3 + 31 + 64 u) = 98
Mass%of phosphoric acid is \(\frac {31}{98}\) × 100 = 31.6%

Question 27.
A burning candle produces a bright flame. At the same time, melted wax gets deposited near the base. [3]
(a) Can physical and chemical changes occur simultaneously? Explain.
(b) In your opinion, is the burning of wax a chemical or physical change?-
(c) Which change is occurring in the melting of wax?
Answer:
(a) In some cases, physical and chemical changes occur together. One such example is the burning of candles. The melting of wax is a physical change. The wax vapours formed bums in air to produce carbon dioxide. This is a chemical change. Thus, burning of candles involves both physical and chemical changes.

(b) The wax vapours combine with oxygen of the air to form a mixture of carbon dioxide and water. This involves a chemical change. So, burning of wax is a chemical change.

(c) The unburnt wax vapours change first to the liquid state and finally to the solid state. This interconversion of states is a physical change.

Question 28.
Rina performed an experiment to observe the behaviour of substances in different states of matter. She took three beakers labelled A, B, and C. [4]
Beaker A contained ice cubes,
Beaker B contained water,
Beaker C contained air trapped under an inverted glass in a water trough.
She observed the shape, volume, and compressibility of the substances over time and recorded her observations in the table below.

Beaker	State of Matter	Shape	Volume	Compressibility
A	Solid	Fixed	Fixed	Negligible
B	Liquid	Takes shape of container	Fixed	Almost negligible
C	Gas	Takes shape of container	Not fixed	High

Answer the following questions based on the above information :
A. Which of the following options correctly compares the compressibility of the three states of matter observed in the experiment?
(a) Solid > Liquid > Gas
(b) Gas > Liquid > Solid
(c) Liquid > Gas > Solid
Justify your answer
Answer:
(b) Gas > Liquid > Solid

Explanation:
Gases are highly compressible due to large intermolecular spaces, liquids have very little compressibility, and solids are nearly incompressible.

B. If beaker A is kept at room temperature, what changes will Rina observe after some time, and why?
Answer:
When beaker A (ice) is kept at room temperature, Rina will observe that the ice melts into water. This happens because ice (solid) absorbs heat from the surroundings and changes into liquid a physical change called melting.

Or

Identify which beaker contains matter that exerts pressure on the walls of the container. Give a reason.
Answer:
Beaker C (gas) contains matter that exerts pressure on the walls of the container.
Reason Gases have particles in constant random motion that collide with the walls of the container, exerting pressure.

C. Rina shook beaker B and noticed the water moved freely. What property of matter does this demonstrate? Which of the following best explains why the substance in beaker C can fill any container completely?
(a) The particles are tightly packed and can only vibrate.
(b) The particles can slide over each other and occupy a fixed volume.
(c) The particles are far apart and move freely in all directions.
(d) The particles have a strong force of attraction.
Answer:
The movement of water when Rina shook beaker B shows that liquids can flow.
Property demonstrated is fluidity, which is the ability of a substance to flow a characteristic property of liquids and gases.
Correct option: (c) The particles are far apart and move freely in all directions.
Explanation This is a defining feature of gases, allowing them to expand and fill the entire volume of any container.

Question 29.
A. Study the given figure and answer the following questions.

(a) What will be the atomic number of X, Y, Z?
(b) Give the mass number of X, Y, and Z. Explain with calculations.
(c) If the K and L-shells of an atom are full, then what would be the total number of electrons in the atom?
(d) What will be the valency of an atom with a fully filled K, L, and M shells?
(e) Name the elements represented by X, Y, and Z.
Answer:
(a) The atomic number of an element is equal to the number of protons. So, the atomic numbers of X, Y, Z will be

Element	Atomic number
X	5
Y	8
Z	15

(b) The mass number of an element is the sum of the number of protons and neutrons present in the nucleus. So, the mass number of X, Y, Z will be

Element	Protons	Neutrons	Mass number
X	5	6	11
Y	8	10	18
Z	15	16	31

One can make mistake in finding out the mass numbers if they do not know the exact relation between mass number, number of protons and number of neutrons.

(c) The maximum number of electrons that K and L shells of an atom can occupy are 2 and 8 respectively. Therefore, if the K and L-shells of an atom are full, then the total number of electrons in the atom would be 2 + 8 = 10 electrons.

(d) If the K, L and M shells of an atom are fully filled, then it can not gain or lose electrons. So, the valency of this element is zero.

Or

B. (a) Give the distribution of maximum electrons for the first three shells.
(b) What is the maximum number of electrons that a shell can have?
(c) How are electrons filled successively in the shells?
(d) What is the maximum electron capacity of an N-shell?
(e) What is the total number of electrons in an atom if its first four shells are completely filled?
Answer:
(a) The maximum number of electrons present in a shell is given by the formula 2n2 , where n is the orbit number of energy level, 1, 2, 3,
For example,
First orbit or X-shell = 2 × (1)² = 2
Second orbit or L-shell = 2 × (2)² = 8
Third orbit or M-shell = 2 × (3)² = 18

(b) The maximum number of electrons that can be accommodated in the outermost orbit is 8.

(c) Electrons are filled in such a way that first all the inner shells are filled one by one. Electrons are not accommodated in a given shell, unless the inner shells are filled.

(d) Maximum electron capacity of N-shell
N-shell is the fourth orbit, i.e., here, n = 4 so, by the formula 2n2, the maximum number of electrons present in N-shell is 2x(4)2 = 32
Hence, 32 is the maximum electron capacity of an N-shell.

(e) If the first four shells (K, L, M, N) of an atom are completely filled, then the total number of electrons are 36 as K,
L, M and N-shell contains a maximum of 2, 8, 8 and 18 electrons respectively.

Section – C

Question 30.
Which of the following statements are correct about mass and weight? [1]
(I) Mass is the amount of matter in an object.
(II) Weight is the force of gravity acting on an object.
(Ill) Mass changes from place to place, but weight remains constant.

Choose the correct option.
(a) (I)
(b) (I) and (II)
(c) (II) and (III)
(d) (I), (II) and (III)
Answer:
(b) (I) and (II)

Explanation
Statement I is correct because mass measures the amount of matter in an object.
Statement II is correct because weight = mass x acceleration due to gravity

Question 31.
Choose the correct option from the below which explains why a moving bus passenger falls forward when the bus suddenly stops? [1]
(a) Due to gravitational force pulling the passenger forward.
(b) Due to inertia of motion, the passenger’s body continues moving forward while the bus stops.
(c) Because air inside the bus pushes the passenger forward.
(d) Because the bus floor becomes slippery.
Answer:
(b) Inertia of motion causes the body to keep moving forward when the bus stops suddenly.

The following cjuestion consists of two statements – Assertion (A) and Reason (R). Answer the question hy 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) Work is said to be done only when a force is applied and the body gets displaced. [1]
Reason (R) Work done is the product of force and displacement of the body in the direction of the force.
Answer:
(a) Both A and R are true, and R is the correct explanation of A.

Explanation:
Both statements are correct, and R explains A as per W = F × d × cos θ. Work is done when force causes displacement in its own direction.

Question 33.
Study the speed-time graph of a body given here and answer the following questions. [2]

State the type of motion that is represented in above diagram.
(i) What is the type of motion represented by OA ?
(ii) What is the type of motion represented by BC ?
(iii) Find out the acceleration of the body.
Answer:
(i) OA is a straight line graph between speed and time and it is sloping upward from O to A.
Therefore, the graph line represents uniform acceleration.

(ii) BC is a straight line graph between speed and time which is sloping downwards from B to C.
Therefore, BC represents uniform retardation or negative acceleration.

(iii) Acceleration of the body as we see from graph line OA represents it, so the slope of velocity time graph OA will give the acceleration of the body.
Thus, Acceleration = Slope of line OA = AD/ OD
We have, AD = 6 m/s, and OD = 4 s
So, acceleration \(\frac{6}{4}\) = 15 m / s²

To ensure full marks, always check the sign of acceleration.

Question 34.
Attempt either A or B.
A. Study the velocity-time graph below and answer the following questions.

(i) What type of motion is represented by the segment OA ?
(ii) Calculate the acceleration of the body in segment AR
Answer:
(i) The segment OA is a straight line with a positive slope. This indicates that the body’s velocity is increasing at a constant rate, which represents uniformly accelerated motion. [1]
(ii) In segment AB, the graph is a horizontal line, meaning the velocity is constant. A horizontal line has a zero slope. Since the slope of a velocity-time graph gives acceleration, the acceleration in this segment is zero.

Or

B. The graph below shows the positions of a body at different time intervals, while travelling from his home to school in the morning. Based on the given graph, answer the following questions

(a) Calculate the speed of the body as it moves from
(i) A to B
(ii) B to C
Answer:
(i) For the motion from point A to B
Time taken, t = 5 – 2 = 3s
Distance covered = 3 – 0 = 3 m
Speed will be during point A to B
= Distance / Time
= \(\frac{3}{3}\)
= 1 m/s

(ii) Similarly, for the motion from point B to C
Time taken, = 7 – 5 = 2 s
Distance covered = 3 – 3 = 0 m
Speed = Distance / Time = \(\frac{0}{2}\) = 0 m/s = 0

(b) Find the time interval during which speed is maximum.
Answer:
Speed in the interval Cto D,
Time taken = 3 s
Distance covered = 8 – 3 = 5 m
Speed will be during point C to D = Distance / Time
= \(\frac{5}{3}\)
= 1.66 m/s

Question 35.
The speed-time graph for a car is shown in the below figure

(i) Shade the area on the graph that represents the distance travelled by the car during the first 4 second.
Answer:
The area under the curve of the speed-time graph gives the distance travelled by an object.

(ii) Which part of the graph represents uniform motion of the car?
Answer:
For uniform motion, the speed-time graph is a straight line parallel to the time axis. So, the straight part of the curve parallel to the time axis represents the uniform motion of the car.

The part of the graph between 6s to 10s represents the uniform motion of the car.

Question 36.
Through what type of medium can . [3]
(i) the transverse waves?
(ii) and the longitudinal waves be transmitted? Explain in brief.
Answer:
(i) Since transverse waves travel in the form of crests and troughs, they involve changes in the shape of medium. So, they can be transmitted through a medium having elasticity of shape. As solids and liquids have elasticity of shape, hence transverse waves can be transmitted through solids and liquids.

(ii) Since, longitudinal waves travel in the form of compressions and rarefactions, they involve changes in the volume and density of the medium. As all media, i.e. solids, liquids and gases have elasticity of volume. Hence these waves (longitudinal waves) can be transmitted through all the three types of media.

Question 37.
(i) What is potential energy? Derive the formula for gravitational potential energy. [3]
(ii) A body of mass 5 kg is raised to a height of 10m. Calculate its potential energy. If the same body is taken to a height double that of the previous one, what will be the new potential energy?
Answer:
(i) Potential energy is the energy possessed by a body due to its position or configuration.
Consider a body of mass ‘m’ at a distance x from the source mass ‘M’. Then the force of attraction between these bodies will be
F = \(\frac{G m M}{x^2}\)
Now consider a small amount of work done in bringing the mass ‘rri without acceleration through a very small distance, dx will be dW = Fdx

∴ Gravitational Potential energy, u_g = \(\frac{-G M m}{r}\)

(ii) Potential energy of a body of mass 5 kg raised to a height of 10 m,
PE = 5 × 9.8 × 10
PE = 490 J
If the height is doubled, h = 2 × 10 = 20 ⇒ PE = 5 × 9.8 × 20
PE = 980 J

Question 38.
Archimedes’ principle, stated as follows: When a body is immersed fully or partially in a fluid, it experiences an upward force that is equal to the weight of the fluid displaced by it. The upward force is known as upthrust or buoyant force. In fact, all objects experience a force of buoyancy when they are immersed in a fluid. The magnitude of this buoyant force depends on the density of the fluid. Objects having density less than that of the liquid in which they are immersed float of the surface of the liquid. If the density of the object is more than the density of the liquid in which it is immersed, then it sinks in the liquid. Hence, body will float or sink depends upon difference between density of body and fluid.

A. Give answer of following questions.
(i) What happens, if the weight of the object is more than the weight of the water displaced by the object?
(ii) Who invented Archimede’s principle?
Answer:
(i) According to the law of floatation, when the weight of the liquid displaced by immersed part of a body is equal to its weight, then a body starts floating. If the weight of the object is more than the weight of the liquid displaced, then the body sinks.
(ii) Archimedes’ a Greek mathematician and physicist invented the Archimede’s principle in the third century BC.

B. What are the application of Archimede’s principle?
Answer:
The following are the application of Archimede’s principle It helps in the design of ships and submarines.
Lactometers utilise it to test the purity of milk

Attempt either C or D
C. A block of wood floats in which with one third of its volume submerged. In oil, the block floats with two thirds of its volume submerged.
Find the density of
(i) wood
(ii) oil, if the density of water is 10³ kg / m³.
Answer:
(i) Let V₀ be the total volume of the block of wood.
We have,
Density of body/ Density of fluid = Volume part of body/ Total volume of body
When the fluid is water, then the volume of immersed part of the wooden block is \(\frac{V_0}{3}\)
Using the formula, Density of wood / Density of water = Volume of immersed part of the wooden block / Total volume of the wooden block
= Density of wood /10³ = (V₃/ 3) / V₀
= Density of wood = 10³ / 3 = 333.33 kg / m3

(ii) When the fluid is oil, then the volume of immersed part of the wooden block is \(\frac{2 V_0}{3}\)
Using the formula, Density of wood/Density of oil = Volume of immersed part of the wooden block/Total volume of the wooden block 333/ Density of oil
= (2V₀/ 3)/ V₀ =2/3
= Density of oil = 500 kg / m³

Or

D. Which is heavier cotton or iron and why?
Answer:
Iron is heavier than cotton because it has a much higher density. For the same volume, iron contains more mass than cotton, making it heavier. Although cotton may look bulkier due to its fluffy structure, its actual mass is less compared to iron. Hence, iron is heavier.

Don’t assume full submersion because the concept applies only when the object is floating, not when it is completely under water.

Question 39.
Attempt either A or B. [5]
A. (i) A shell is fired from a canon vertically upwards from a point X as shown in the figure below. On reaching the highest point Y, it falls down. Give brief about the transformation of energy from X to Y and Y to X.
(ii) A shell of mass 2 kg is dropped from a height of 40 m. Calculate its kinetic energy and potential energy after 1st second.
(iii) Calculate KE and potential energy after 2nd of 3rd sec.
(iii) Calculate KE and potential energy after 2nd of 3rd sec.

Answer:
(i) While going vertically upwards from ground, kinetic energy changes to potential energy and becomes maximum at point Y. When going down from the highest point, potential energy changes to kinetic energy and it becomes maximum just before hitting the ground.

(ii) Total energy of the shell, TE = mgh = 2 × 10 × 40 = 800 J
After 1st second, = u+ gt = 0 + 10 × 1= 10 m/s (u = 0 at point Y)
Kinetic energy, KE = \(\frac{1}{2}\) × m × v²
\(\frac{1}{2}\) × 2 × 10² = 100J
Potential energy, PE = TE – KE = 800 – 100 = 700 J

(iii) After 2nd second,
v = u + gt = 0 + 10 × 2
v = 20 m/s
KE = \(\frac{1}{2}\)mv² = \(\frac{1}{2}\) × 2 × 20² = 400J
PE = TE – KE = 800 – 400 = 400J

After 3rd second,
Using s = ut + \(\frac{1}{2}\)gt²
40 = 0 × t + \(\frac{1}{2}\) × 10 × t²
\(\frac{80}{10}\) = t²
⇒ t = 2.82 s
The shell falls back to ground in 2.82 s, so after 3 s, it will have energy equal to total energy due to law of conservation of energy.

Or

B. Represent graphically by two separate diagrams in each case.
(i) Two sound waves having the same amplitude but different frequencies.
Answer:

In both cases (a) and (b), same amplitude and difference frequencies, i.e (A = A)

(ii) Two sound waves having the same frequency but different amplitudes.
Answer:

In both the cases, (a) and (b), same frequency and different amplitudes, i.e. (A₁ ≠ A₂).

(iii) Two sound waves having different amplitudes and also different wavelengths.
Answer:

In both cases (a) and (b), different amplitudes and different wavelengths, i.e A₁A₂, λ₁λ₂.