Key Concept: Force and Interaction

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that when a football player kicks a ball, the ball moves in the direction of the kick. This is true because applying a force (kick) causes the ball to move. The reason states that a force is a push or pull resulting from the interaction between two objects, which is also true as per the definition of force. Moreover, the reason correctly explains why the ball moves—because the player's foot interacts with the ball, applying a force that sets it in motion.

Key Concept: Balanced Forces

c) The forces are balanced
[Solution Description]
If an object is at rest, it means the net force acting on it is zero \(F_{\text{net}} = 0\), i.e., all forces are balanced. As mentioned in the syllabus: "It means that the forces acting on the object are balancing one another."
This implies no unbalanced force is acting, not that no force is present.

Key Concept: Definition of Force

b) A push or pull on an object due to its interaction with another object
[Solution Description]
A force is defined as a push or pull on an object resulting from its interaction with another object. It can change an object's speed, direction of motion, or shape.

Key Concept: Force, Change in Motion

c) A force acted on the car to change its direction without changing its speed.
[Solution Description]
The question involves understanding the effect of force on an object's motion. Force can change the direction of motion without changing the speed. In this case, since the car's speed remains the same but its direction changes, a force must have acted perpendicular to the initial direction of motion. This force causes the change in direction but does not affect the magnitude of velocity.
Step-by-step reasoning:
1. Initially, the car moves at $10 \, \text{m/s}$ in one direction.
2. After the change, it moves at $10 \, \text{m/s}$ in a perpendicular direction.
3. Since the direction changed, a force must have acted on the car to cause this change, even though the speed remained the same.

Key Concept: Push and Pull Forces, Force Interactions

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that pushing requires more force than pulling for moving a heavy box. This is because when you push, part of your force adds to the weight of the box, increasing the normal force and thus increasing friction. On the other hand, when you pull, the vertical component of the force lifts the box slightly, reducing the normal force and hence decreasing friction. Therefore, both Assertion and Reason are true, and the Reason correctly explains the Assertion.

Key Concept: Types of Force

c) A person lifting a heavy bag
[Solution Description]
Muscular force is the force exerted by muscles when they contract or elongate. Lifting a bag involves the use of arm muscles to apply an upward pull, making it a clear example of muscular force. The other options involve non-muscular forces like magnetic or gravitational forces.

Key Concept: Definition of Force

b) A push or pull applied on an object
[Solution Description]
A force is defined as a push or pull applied on an object resulting from its interaction with another object. This definition aligns with the basic understanding derived from common experiences like pushing a box or pulling a drawer.

Key Concept: Effect of Force

c) Changing the object's color
[Solution Description]
Forces can cause various effects: making an object move from rest, changing its speed or direction, or altering its shape. However, force does not change the color of an object, as this property is unrelated to mechanical interactions.

Key Concept: Force interaction, Effects of force

b) Speed decreases, direction remains same initially
[Solution Description]
The wind applies a contact force opposite to the bicycle's motion. According to force concepts: 1) The bicycle was moving at constant speed (balanced forces). 2) Wind introduces unbalanced force opposite to motion. 3) This will cause deceleration (speed decreases) while maintaining same direction initially. If wind continues, it may eventually stop or reverse direction.

Key Concept: Muscular force, Contact forces

c) Contact forces act both during lifting and holding
[Solution Description]
When lifting: 1) Muscular force overcomes gravity (contact force through hands). 2) Forces are unbalanced during lifting. 3) When stationary: muscular force equals gravitational pull (balanced forces). 4) Only contact forces act throughout - muscles (biological) and normal force. The barbell doesn't move because forces balance.

Key Concept: Definition of Force

c) A push or pull applied on an object
[Solution Description]
According to the syllabus, a force is defined as a push or pull applied on an object resulting from the object's interaction with another object. The SI unit of force is newton ($N$).
Therefore, the correct choice is the option that mentions "push or pull" as the scientific definition of force.

Key Concept: Examples of Force

c) Pedaling a bicycle to move forward
[Solution Description]
From the syllabus, examples of force include moving a box by pushing or pulling and pedaling a bicycle. These actions involve applying a push or pull.
Thus, the correct answer should describe an action involving push or pull.

Key Concept: Effects of Force on Objects

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The Assertion states that a force can change the speed of a moving object, which is true as per the syllabus (e.g., hitting a ball changes its speed). The Reason states that applying brakes on a bicycle reduces its speed by applying frictional force, which is also true and directly explains the Assertion because friction (a type of force) opposes motion, reducing speed. Thus, both are true, and the Reason correctly explains the Assertion.

Key Concept: Force, Change in Shape, Application

d) The rod changes shape (either stretches or compresses).
[Solution Description]
When two equal and opposite forces are applied along the length of a metal rod, they create a balanced force scenario. However, depending on the material's elasticity, the rod may experience a change in shape, such as elongation or compression. Since the forces are equal and opposite, the net force is zero, but the rod's shape can still change due to the internal stress caused by the applied forces.

Key Concept: Effects of Force

d) It changes the direction of the ball's motion
[Solution Description]
When a bat hits a moving ball, it applies a force that can change the direction of the ball. This demonstrates one of the effects of force—changing the direction of motion of an object.

Key Concept: Force and its Effects

d) Assertion is false, but Reason is true.
[Solution Description] The Assertion states that a force applied to a stationary object will always cause it to move in the direction of the applied force. This is not entirely true because if the applied force is balanced by another force (e.g., friction), the object may not move. The Reason correctly states that force is required to change the state of rest or motion of an object, as per Newton's First Law of Motion. Therefore, while the Reason is correct, the Assertion is partially false.

Key Concept: Change in Shape Due to Force

b) Pressing an inflated balloon.
[Solution Description]
Forces can change the shape of an object when applied. Pressing an inflated balloon deforms its shape, which matches the given syllabus example where applying push on a balloon changes its shape. The other options involve changes in motion or stopping an object, not shape deformation.

Key Concept: Effect of Force

b) It brings the ball to rest
[Solution Description]
When a fielder stops a moving cricket ball by catching it, the force applied opposes the motion of the ball, causing it to slow down and eventually stop. This means the force decreases the speed of the ball.

Key Concept: Effect of force on motion and shape

d) Assertion is false, but Reason is true.
[Solution Description]
The assertion states that a fielder stopping a cricket ball changes its speed but not its direction. This is partially correct because when a fielder catches a ball, they apply a force opposite to the ball's motion, which primarily reduces its speed. However, if the force is not perfectly aligned with the ball's initial motion, it can also slightly alter the direction.
The reason states that when a force is applied opposite to the direction of motion, it decreases the speed of the object. This is true as per Newton's laws of motion. However, the reason does not fully explain why the assertion claims no change in direction, because in practical scenarios, minor directional changes can occur.
Thus, the assertion is not entirely accurate because the direction may change slightly, while the reason is true but does not completely justify the assertion.

Key Concept: Effect of force on motion and shape

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that applying a force by pulling a moving bicycle from behind stops the bicycle. This is correct as per the syllabus, which mentions that force can stop or decrease the speed of a moving object (as seen in Table 5.1, example 1). The reason states that a force can change the speed or bring an object to rest, which is also true according to the syllabus. Furthermore, the reason correctly explains why the assertion occurs—pulling force changes the speed, leading to stopping the bicycle. Thus, both are true, and the reason explains the assertion.

Key Concept: Effects of Force on Objects

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that when a footballer kicks a stationary football, the force applied causes it to move. This is true because applying a force on a stationary object can set it into motion as per the syllabus (e.g., making an object move from rest). The reason states that a force can make an object move from rest, which is also correct as mentioned in the syllabus. Moreover, the reason correctly explains why the assertion occurs—the force applied by the kick overcomes inertia, causing the football to move from rest. Thus, both are true, and the reason is the correct explanation.

Key Concept: Assertion-Reason

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.
[Solution Description]
The assertion states that a force can change the direction of motion of a moving object, which is true as seen in examples like hitting a ball with a bat. The reason states that when a fielder stops a moving ball, the force applied changes its speed, which is also true. However, the reason does not correctly explain the assertion because the assertion is about changing direction while the reason is about changing speed. Therefore, both are true but the reason does not explain the assertion.

Key Concept: Change in motion, Direction of force

c) The ball moves northwest with a force of approximately 58 N
[Solution Description]
To find the net effect on the ball's motion:
Step 1: The ball is initially stationary. The northward force (50 N) will make it move north.
Step 2: The westward force (30 N) acts perpendicularly to the northward force.
Step 3: The resultant direction will be northwest since both forces combine vectorially.
Step 4: The magnitude of the resultant force can be calculated using the Pythagorean theorem: $\sqrt{50^2 + 30^2} = \sqrt{2500 + 900} = \sqrt{3400} \approx 58.31$ N.
Therefore, the ball will move in the northwest direction with a force of approximately 58.31 N.

Key Concept: Effect of Force

b) The ball changes its direction.
[Solution Description]
Hitting a moving ball with a bat applies a force to the ball. This force changes the direction of the ball's motion, as seen in sports like cricket or baseball.

Key Concept: Force and Interaction

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that a force is a push or pull resulting from interaction, which is true as per the syllabus definition of force. The reason states forces arise only when two objects interact, which is also true and directly explains why forces are interactions between objects. Hence, both are true, and the reason correctly explains the assertion.

Key Concept: Force Definition

c) There must be an interaction between the objects
[Solution Description]
A force arises due to the interaction between two or more objects. Without interaction, no force exists. For example, a book on a table experiences gravitational force only because it interacts with the Earth.

Key Concept: Types of Forces

c) Gravitational force
[Solution Description]
Non-contact forces act without direct physical contact. Examples include gravitational force, magnetic force, and electrostatic force, whereas muscular and frictional forces require contact.

Key Concept: Force as Interaction, Newton's Third Law

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that when a book is placed on a table, the table exerts an equal and opposite force on the book. This is true because forces arise due to interaction between two objects. The reason mentions Newton's third law, which states that for every action, there is an equal and opposite reaction. Since both the assertion and reason are correct, and the reason correctly explains why the table exerts an equal and opposite force on the book, the correct option is (a).

Key Concept: Interaction Between Objects

b) Pushing a table with your hand
[Solution Description]
A force arises when two objects interact with each other, such as pushing a table where your hand applies a force on the table.

Key Concept: Balanced Forces

d) Assertion is false, but Reason is true.
[Solution Description] The Assertion states that an object at rest implies no forces are acting on it, which is false because an object at rest can have balanced forces acting on it. The Reason correctly explains that balanced forces result in no change in the state of motion, but since the Assertion is false, this does not matter. Thus, Answer is: Assertion is false, but Reason is true.

Key Concept: Force Interaction

c) A magnet attracting a paperclip.
[Solution Description]
Forces arise due to interactions between two objects. A magnet attracting a paperclip involves an interaction between the magnet (one object) and the paperclip (another object), resulting in a magnetic force.

Key Concept: Force Interaction

c) Balanced forces are acting on the book.
[Solution Description]
The book is at rest, which means the forces acting on it are balanced. The gravitational force pulling the book downward is equal in magnitude but opposite in direction to the normal force exerted by the table pushing the book upward.

Key Concept: Non-Contact Force

c) Gravitational force
[Solution Description]
Non-contact forces act without physical contact between objects. Examples include gravitational force, magnetic force, and electrostatic force. Frictional force requires direct contact between surfaces, making it a contact force.

Key Concept: Force as Interaction

c) A push or pull resulting from the interaction between two or more objects
[Solution Description]
A force is a push or pull resulting from the interaction between two or more objects.

Key Concept: Balanced Forces

d) The forces are balanced, cancelling each other out
[Solution Description]
When an object is at rest, the forces acting on it are balanced, meaning they cancel each other out.

Key Concept: SI Unit of Force

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that the SI unit of force is newton ($N$), which is correct as per the syllabus. The reason states that force is an interaction involving a push or pull between two objects, which is also true. Moreover, the reason correctly explains why the unit is named newton since it quantifies such interactions.

Key Concept: Force Characteristics

c) The force disappears
[Solution Description]
According to the concept of forces, they exist only during the interaction between objects. When the interaction stops, the force ceases to act on both objects. The correct answer is that the force disappears.

Key Concept: Force existence conditions

d) Two neutral particles at rest far apart in space
[Solution Description]
Forces only exist when two objects interact. If there is no physical contact or field interaction (like gravity, electromagnetism), no force exists. A magnet not touching a nail has no contact force, but still experiences magnetic force at a distance. Truly no force exists only when there is no interaction whatsoever.

Key Concept: Force Interaction between Objects

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
According to the concept of forces, whenever two objects interact, each object experiences a force from the other. The assertion states that when you push a table with your hand, both the hand and the table experience a force, which is true. The reason states that a force is always an interaction between two objects, which is also true and correctly explains the assertion. Therefore, both the assertion and reason are true, and the reason is the correct explanation of the assertion.

Key Concept: Force Interaction Requirement

b) A magnet attracting an iron nail from a distance.
[Solution Description]
A force requires interaction between two objects. A book resting on a table interacts with the table via normal force and gravitational force. The other options either involve only one object or do not describe a force interaction.

Key Concept: Gravitational Force

b) Newton
[Solution Description]
Weight is the gravitational force with which the Earth attracts an object. The SI unit of weight (and force in general) is the newton, represented by the symbol $N$.

Key Concept: Magnetic force, Electrostatic force

d) Both non-contact forces act simultaneously
[Solution Description]
The iron ball experiences magnetic attraction regardless of charge due to its ferromagnetic property. If charged, it also experiences electrostatic force - repulsion if like-charged with the magnet, attraction if oppositely charged. The net force depends on relative strengths, but both non-contact forces are always present.

Key Concept: Muscular force, Gravitational force

c) Both contact and non-contact forces act in opposite directions
[Solution Description]
The weightlifter applies muscular force to lift the barbell. The gravitational force acts downward with magnitude F = mg = 100 kg × 9.8 m/s$^2$ = 980 N. The upward muscular force must overcome this gravitational force. The calculation shows both contact (muscular) and non-contact (gravitational) forces are involved.

Key Concept: Contact and Non-Contact Forces

d) Assertion is false, but Reason is true.
[Solution Description]
Assertion states that magnetic force is a contact force, but this is incorrect because magnetic force is a non-contact force as it acts without physical interaction. Reason correctly states that contact forces require physical interaction. Thus, Assertion is false, but Reason is true.

Key Concept: Contact Forces

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The Assertion states that friction is a type of contact force, which is true because friction requires physical contact between two surfaces to act. The Reason explains why friction is a contact force by stating that it acts only when two surfaces are in physical contact. Since both statements are correct and the Reason correctly explains the Assertion, the answer is option (a).

Key Concept: Assertion-Reason

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The Assertion states that frictional force always opposes the relative motion between two surfaces in contact, which is true because friction acts in the direction opposite to the motion or attempted motion of an object. The Reason explains that frictional force arises due to microscopic irregularities and interlocking between surfaces, which is also true and correctly explains why friction opposes motion. Therefore, both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

Key Concept: Electrostatic Force, Non-contact Forces

d) 80 N
[Solution Description]
Apply Coulomb's law:
$F = k \frac{|q_1 q_2|}{r^2}$
Convert units: $q_1 = 4 \times 10^{-6} \, \text{C}$, $q_2 = 2 \times 10^{-6} \, \text{C}$, $r = 0.03 \, \text{m}$.
$F = 9 \times 10^9 \times \frac{|4 \times 10^{-6} \times (-2) \times 10^{-6}|}{(0.03)^2}$
$F = 9 \times 10^9 \times \frac{8 \times 10^{-12}}{9 \times 10^{-4}} = 80 \, \text{N}$

Key Concept: Contact Forces

c) Muscular force used to lift a bag
[Solution Description]
Muscular force and friction are both contact forces as they require physical interaction between objects. Magnetic force does not require contact.

Key Concept: Muscular Force

d) A ball falling to the ground.
[Solution Description]
Muscular force requires the involvement of muscles for actions like walking, chewing, or lifting. Activities not requiring muscles, such as falling under gravity, do not use muscular force.

Key Concept: Muscular Force

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that muscular force is an example of a contact force, which is true because muscular force acts only when there is physical contact between the body and the object. The reason given is also true since muscular force indeed occurs only when muscles interact physically with an object. Moreover, the reason correctly explains why muscular force is considered a contact force. Therefore, both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

Key Concept: Muscular force, External applications

c) Muscular force, as the oxen contract their muscles to move
[Solution Description]
Oxen use their muscles to generate the force required to pull the plow. Since muscular force is defined as the force resulting from muscle action, the oxen's effort to move the plow is a direct application of muscular force.

Key Concept: Muscular Force

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that muscular force is a type of contact force, which is true because muscular force is exerted through muscles and requires direct physical contact. The reason explains why muscular force is a contact force by stating that it requires direct physical contact, which correctly justifies the assertion. Therefore, both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

Key Concept: Friction and Surface Texture

a) Glass surface because it has lower friction.
[Solution Description]
Friction depends on the roughness of the surfaces in contact. Glass is smoother than sandpaper, so the frictional force acting on the block is less on the glass surface compared to the sandpaper surface. With lower friction, the block can travel farther before stopping.

Key Concept: Friction, Air Resistance

c) Assertion is true, but Reason is false.
[Solution Description]
The assertion states that aeroplanes are designed with streamlined shapes to minimize air resistance, which is true. Streamlining reduces the drag force (a type of friction) caused by air molecules colliding with the surface of the aeroplane. However, the reason claims that friction due to air acts in the same direction as the motion of the aeroplane, which is false. Friction always opposes the relative motion between surfaces or objects and thus air resistance acts opposite to the direction of motion of the aeroplane.

Key Concept: Friction, Surface Irregularities, Real-World Application

b) 20 N
[Solution Description]
To move the block, the applied force must overcome the static friction. The formula for maximum static friction is $f_s = \mu_s \times N$, where $\mu_s$ is the coefficient of static friction and $N$ is the normal force. Here, the normal force equals the weight of the block, i.e., $N = 50\, \text{N}$. Substituting $\mu_s = 0.4$, we get $f_s = 0.4 \times 50 = 20\, \text{N}$. Thus, the minimum force required to start moving the block is 20 N.

Key Concept: Friction, Multi-Surface Comparison, Numerical Difficulty

c) $2.4\, \text{m/s}^2$
[Solution Description]
The forces acting on the box are gravity ($mg \sin\theta$) down the incline and kinetic friction ($f_k = \mu_k N$) opposing motion. Normal force $N = mg \cos\theta$. Net force along the incline is $F_{\text{net}} = mg \sin\theta - \mu_k mg \cos\theta$. Acceleration $a = \frac{F_{\text{net}}}{m} = g (\sin\theta - \mu_k \cos\theta)$. Substituting $\theta = 30^\circ$, $\sin30^\circ = 0.5$, $\cos30^\circ \approx 0.866$, and $\mu_k = 0.3$, we get:
$a = 10 (0.5 - 0.3 \times 0.866) = 10 (0.5 - 0.2598) = 10 \times 0.2402 \approx 2.402\, \text{m/s}^2.$

Key Concept: Gravitational force, Non-contact forces

c) In both locations, the objects hit the ground simultaneously if air resistance is negligible
[Solution Description]
On the Moon, both objects would fall at the same rate because gravitational acceleration is independent of mass in a vacuum. This demonstrates the universal nature of gravitational force as a non-contact force. However, on Earth, air resistance affects the feather more significantly, making it appear to fall slower - but in reality, gravitational acceleration is the same for both objects without atmospheric interference.

Key Concept: Magnetic force, Gravitational force

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.
[Solution Description]
The Assertion states that a magnet can attract an iron nail without touching it, which is true because magnetic force acts at a distance (non-contact). The Reason states that gravitational force is a non-contact force, which is also true as the Earth pulls objects without direct contact. However, the Reason does not explain why the Assertion is correct since gravitational force and magnetic force are two different phenomena. Thus, both statements are true, but the Reason does not correctly explain the Assertion.

Key Concept: Gravitational Force

d) The ball falls back to the ground after reaching a certain height.
[Solution Description]
Earth's gravitational force acts as a non-contact force, pulling all objects toward its center. Whether thrown lightly or hard, the ball will always return to the ground due to this attraction.

Key Concept: Electrostatic Force

b) They repel each other
[Solution Description]
When two balloons are rubbed with a woollen cloth, they acquire like charges. According to the principle of electrostatics, like charges repel each other, so the balloons will repel each other when brought close.

Key Concept: Magnetic Force - Attraction/Repulsion

b) They repel each other
[Solution Description]
According to the properties of magnetic force, like poles (North-North or South-South) repel each other. The repulsive force causes the magnets to push away from each other.

Key Concept: Magnetic force, Pole interaction

b) 4 North and 4 South poles
[Solution Description]
Every magnet has a North and South pole, regardless of its size. When a bar magnet is broken, each piece becomes a new magnet with its own North and South poles. Breaking one magnet into four pieces will create four new magnets, each with a North and South pole. Thus, there will be 4 North poles and 4 South poles, totaling 8 poles.

Key Concept: Magnetic force

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
According to the syllabus, when two magnets are brought close to each other, like poles (North-North or South-South) repel each other. This is because the magnetic force between like poles is repulsive. Hence, both Assertion and Reason are true, and Reason correctly explains Assertion.

Key Concept: Magnetic Force - Non-contact nature

b) It can act over a distance without physical contact
[Solution Description]
Magnetic force acts over a distance without requiring any physical contact between the interacting objects. This characteristic classifies it as a non-contact force.

Key Concept: Electrostatic Force - Attraction and Repulsion

c) Assertion is true, but Reason is false.
[Solution Description]
The Assertion states that a charged balloon repels another similarly charged balloon, which is true as per the observation in Activity 5.7 where two rubbed balloons repel each other. The Reason claims that like charges attract each other, but according to the inference from the activity, like charges repel each other, not attract. Hence, the Assertion is true, but the Reason is false.

Key Concept: Electrostatic Force: Charging by Rubbing

c) It transfers electrons from polythene to the straw, charging it negatively.
[Solution Description]
Rubbing two materials together causes friction, which transfers electrons from one material to another. In this case, electrons are transferred from the polythene to the plastic straw, leaving the straw negatively charged and the polythene positively charged. This creates an electrostatic force.

Key Concept: Electrostatic force, charge transfer

c) Sphere B becomes negatively charged
[Solution Description]
When the positively charged Sphere A is brought near Sphere B, it induces negative charges on Sphere B's near side and positive charges on its far side. Grounding Sphere B allows the repelled positive charges to escape, leaving Sphere B with a net negative charge after removing the ground. Thus, Sphere B becomes negatively charged.

Key Concept: Like and Unlike Charges

c) Like charges repel each other
[Solution Description]
When two similarly charged objects repel each other, it indicates that like charges repel. This is a fundamental property of electrostatic force.

Key Concept: Gravitational Force Definition

a) Gravitational force
[Solution Description]
The force with which the Earth attracts objects towards itself is called gravitational force. It is also known as gravity or weight when referring to the object being pulled.

Key Concept: Gravitational force, Weight, Non-contact force

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.
[Solution Description]
The Assertion states that the weight of an object on the Moon is less than its weight on Earth due to the weaker gravitational force of the Moon. This is true because the table in the syllabus shows the weight of a $1 \, kg$ object is $1.6 \, N$ on the Moon compared to $10 \, N$ on Earth. The Reason states that gravitational force is a non-contact force and varies with the mass of the celestial body. This is also true as gravitational force acts without contact and differs based on the mass of the planet or moon (e.g., Jupiter's gravitational force is much stronger). However, the Reason does not directly explain why the Moon’s gravitational force is weaker; it merely states facts about gravitational force. Thus, both statements are true, but the Reason is not the correct explanation of the Assertion.

Key Concept: Gravitational force, Spring balance principle

b) 19 N
[Solution Description]
First, find the mass of the object using Earth's gravity: $Weight = mass \times g_{Earth}$. Given $Weight_{Earth} = 49 N$ and $g_{Earth} = 9.8 m/s^2$, so $mass = \frac{49}{9.8} = 5 kg$. On Mars, the weight would be $Weight_{Mars} = mass \times g_{Mars}$. From the table, for $1 kg$ mass, weight on Mars is $3.8 N$. Thus, for $5 kg$, weight on Mars would be $5 \times 3.8 = 19 N$.

Key Concept: Vertical Motion Under Gravity

c) 20 m
[Solution Description]
When the ball is thrown vertically upward, its speed gradually decreases because gravity pulls it downward. At the highest point, the ball stops for a moment before falling back down. Since the initial velocity is 20 m/s and gravity is 10 m/s², the ball will rise to a maximum height of 20 metres before it starts falling back down.

Key Concept: Difference Between Mass and Weight

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
Mass is an intrinsic property of an object and represents the quantity of matter it contains. This value does not depend on the gravitational force acting on the object, so it remains constant regardless of whether the object is on Earth, the Moon, or any other celestial body. On the other hand, weight is the force exerted by gravity on that mass, calculated as $W = m \times g$, where $g$ varies depending on the celestial body. Therefore, the Assertion is true because mass is independent of location. The Reason is also true and correctly explains the Assertion since it states that mass is the amount of matter, which does not change.

Key Concept: Weight Measurement, Gravitational Force

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
Step 1: Understand the concept of weight. Weight ($W$) is given by the formula $W = m \times g$, where $m$ is mass and $g$ is acceleration due to gravity.
Step 2: Analyze the Assertion. Since $g$ on the Moon ($1.6$ m/s²) is less than $g$ on Earth ($10$ m/s²), for a given mass $m$, the weight $W$ will indeed be less on the Moon than on Earth. Thus, the Assertion is true.
Step 3: Examine the Reason. The Reason states the correct values of $g$ for the Moon and Earth, which are accurate. It also correctly explains why the weight differs between the two celestial bodies. Hence, the Reason is true and provides a valid explanation for the Assertion.

Key Concept: Spring Balance Measurement

b) $0.1 N$
[Solution Description]
The smallest measurable weight is calculated by dividing the range by the number of divisions: $\frac{1 N - 0 N}{10} = 0.1 N$.

Key Concept: Spring balance calibration, weight measurement

c) 0.1 N
[Solution Description]
The spring balance has major marks at every 1 N interval (e.g., 0 N, 1 N, 2 N etc.). Between each major mark there are 10 divisions. To find the smallest measurable weight change:
Weight difference per division = Total difference between major marks / Number of divisions = 1 N / 10 = 0.1 N
Therefore, the smallest measurable weight change is 0.1 N.

Key Concept: Mass vs. Weight

b) 1 kg
[Solution Description]
From the table, 1 kg mass corresponds to 25.4 N on Jupiter. Therefore, an object weighing 25.4 N has a mass of 1 kg since weight is directly proportional to mass under the same gravitational force.

Key Concept: Weight Measurement and Gravitational Force

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that the weight of an object on the Moon is less than its weight on Earth, which is true because weight depends on the gravitational force acting on the object. The reason explains that the gravitational force on the Moon is weaker than on Earth, which is also true and correctly justifies the assertion. This is evident from the given table where 1 kg mass weighs 1.6 N on the Moon compared to 10 N on Earth. Therefore, both the assertion and reason are true, and the reason is the correct explanation of the assertion.

Key Concept: Weight Definition

c) Newton (N)
[Solution Description]
Weight is defined as the force with which the Earth pulls an object towards itself. Since it is a force, its SI unit is newton (N).

Key Concept: Weight and Its Measurement, Weight Measured in Newtons

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
Weight is the force exerted by gravity on an object and is given by $W = m \times g$, where $m$ is mass (constant) and $g$ is gravitational acceleration (varies with location). On Earth, $g = 9.8 \, \text{m/s}^2$, while on Mars, $g = 3.7 \, \text{m/s}^2$. Thus, weight changes with location. The reason correctly explains why weight differs due to varying gravitational forces, making both Assertion and Reason true with a valid explanation.

Key Concept: Difference between Mass and Weight

c) Mass remains constant, but weight changes depending on gravity.
[Solution Description]
Mass is the amount of matter in an object and remains constant, while weight depends on gravitational force and can vary.

Key Concept: Weight calculation on different planets

a) 76.2 N
[Solution Description]
The weight on Jupiter is calculated by multiplying the gravitational ratio (2.54) by the weight on Earth. Therefore, $30 \, \text{N} \times 2.54 = 76.2 \, \text{N}$.

Key Concept: Mass vs. Weight

c) Mass remains constant, but weight changes depending on the gravitational field.
[Solution Description]
Mass is the amount of matter in an object and remains constant regardless of location. Weight is the gravitational force acting on the object, which varies with the gravitational field strength. The SI unit of mass is kilogram ($\text{kg}$), while the SI unit of weight is newton ($\text{N}$).

Key Concept: Definition of Weight

c) newton ($N$)
[Solution Description]
The SI unit of weight is newton ($N$), as weight is a force measured in the same unit as force.

Key Concept: Measurement of weight, spring balance calibration

c) 0.1 N
[Solution Description]
The difference between two major marks = 1 N. Number of divisions between them = 10. Therefore, smallest measurement = $\frac{1 N}{10} = 0.1 N$.

Key Concept: Weight Measurement Principle

c) By measuring the extension of the spring due to the weight
[Solution Description]
A spring balance measures weight by the stretching of its spring when an object is hung from it. The amount of stretch corresponds to the weight of the object.

Key Concept: Measurement of weight using a spring balance

c) 0.1 N
[Solution Description]
The difference between two major marks is 0.5 N (since there are 10 divisions from 0 N to 5 N: $\frac{5 \, \text{N}}{10} = 0.5 \, \text{N}$). Each major division has 5 smaller divisions, so the smallest division represents $\frac{0.5 \, \text{N}}{5} = 0.1 \, \text{N}$. Hence, the smallest weight measurable is 0.1 N.

Key Concept: Measurement of weight using a spring balance

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
- The assertion states that the smallest measurable value depends on the divisions between two bigger marks, which is true as per the syllabus.
- The reason correctly explains this by providing the calculation: $\frac{1 N}{5} = 0.2 N$, showing how the smallest division is derived.
- Hence, both the assertion and reason are true, and the reason correctly explains the assertion.

Key Concept: Floating and Sinking

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
When an object is placed in water, it displaces water equal to its own volume. According to Archimedes' Principle, the buoyant force (upthrust) acting on the object is equal to the weight of the displaced water. If the weight of the displaced water is less than the weight of the object, the buoyant force will be insufficient to counteract the gravitational force, causing the object to sink. In this case, the plastic bottle filled with sand has a higher density compared to water, so it sinks because the weight of the displaced water is less than the weight of the bottle. Thus, both Assertion and Reason are true, and the Reason correctly explains the Assertion.

Key Concept: Archimedes’ Principle

c) The weight of the liquid displaced by the object
[Solution Description]
Archimedes’ Principle states that the buoyant force acting on an object immersed in a liquid is equal to the weight of the liquid displaced by the object.

Key Concept: Density Comparison, Floating Condition

b) $\rho_A > \rho_w > \rho_C > \rho_B$
[Solution Description]
According to floating conditions:
1. For sinking object: $\rho_A > \rho_w$
2. For partially floating object: $\rho_B = \frac{1}{2}\rho_w$ (since half volume displaces equal weight)
3. For fully floating object: $\rho_C \rho_w > \rho_C > \rho_B$

Key Concept: Density Effect

b) Increases the buoyant force
[Solution Description]
Buoyant force is directly proportional to the density of the liquid. Increasing the density of the liquid increases the buoyant force acting on the object.

Key Concept: Floating Condition

b) When the weight of displaced liquid is equal to its own weight
[Solution Description]
Archimedes' Principle states that an object floats if the weight of the displaced liquid equals the object's weight. If the buoyant force balances the gravitational force, the object remains afloat.

Key Concept: Density and Buoyancy

a) Higher density increases buoyant force
[Solution Description]
The buoyant force depends on the density of the liquid. A denser liquid exerts a greater buoyant force because it can displace more mass for the same volume compared to a less dense liquid.

Key Concept: Buoyant Force

b) Upward
[Solution Description]
The buoyant force is the upward force exerted by a liquid on an object immersed in it, as observed when pushing a plastic bottle into water. This force opposes the gravitational force acting downward.

Key Concept: Archimides’ Principle

c) 20 N
[Solution Description]
The buoyant force is equal to the loss in weight of the object when submerged in the liquid.
Weight in air: $W_{air} = 50 \, \text{N}$
Weight in water: $W_{water} = 30 \, \text{N}$
Buoyant force ($F_b$) = $W_{air} - W_{water} = 50 - 30 = 20 \, \text{N}$

Key Concept: Archimedes' Principle, Density

d) 1.00
[Solution Description]
Let h be the height submerged in water. The volume submerged is $V_s = (0.1)^2 \times h$. The weight of displaced water plus oil equals the block's weight: $\rho_w V_s g + \rho_o ((0.1)^3 - V_s)g = \rho_b (0.1)^3 g$. Substituting values: $(1000)(0.01h)g + (800)(0.001 - 0.01h)g = (600)(0.001)g$. Simplifying: $10h + 0.8 - 8h = 0.6$ → $2h = -0.2$ → $h = 0.1$ m = 10 cm. Thus, the entire block is submerged in water.

Key Concept: Buoyant Force

c) Buoyant force is equal to the weight
[Solution Description]
When an object floats, it means the buoyant force equals the object's weight. This balance allows the object to stay afloat without sinking or rising further. So, if an object is floating, the buoyant force is equal to its weight.

Key Concept: Density Comparison

c) Density of A is greater than density of B
[Solution Description]
For an object to float, its average density must be less than or equal to the density of water ($1000 \text{ kg/m}^3$). If an object sinks, its density is greater than that of water. Therefore:
$\text{Density of A} > \text{Density of water} > \text{Density of B}.$

Key Concept: Density and Floating

c) It has lower density than water
[Solution Description]
Pumice stone floats because it has a lower density than water. It contains tiny air pockets trapped inside during volcanic eruptions, making it porous and lighter than water. Hence, it displaces enough water to create a buoyant force equal to its own weight, allowing it to float.