Key Concept: Force Definition

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. It can change the speed, direction of motion, or shape of the object.
The correct answer corresponds to the definition provided in the syllabus: "Generally, the push or pull applied on an object is called force in science."

Key Concept: Effects of Force

d) Changes speed, direction, or shape of the object
[Solution Description]
According to the syllabus, the application of force can:
1. Make an object move from rest.
2. Change the speed of a moving object.
3. Change the direction of motion of an object.
4. Change the shape of the object.
All these effects are summarized correctly in one of the options.

Key Concept: Force, Multiple Effects

c) The ball slows down and may reverse direction depending on its mass.
[Solution Description]
The question combines concepts of force, deceleration, and change in motion. On a frictionless surface, the only force acting is the applied $2 \, \text{N}$. Using Newton’s second law ($F = ma$), we find the deceleration ($a = F/m$, assuming mass $m$). The change in velocity ($v = u + at$) will show how the ball’s speed and direction are affected over the $3 \, \text{s}$ interval.
Step-by-step calculations:
1. Deceleration: $a = F/m = 2 \, \text{N} / m$.
2. Final velocity: $v = 4 \, \text{m/s} - (2/m \times 3) = 4 - 6/m \, \text{m/s}$.
3. If $6/m > 4$, the ball stops and reverses direction; else, it slows down.

Key Concept: Force, Friction, Interaction of Forces

d) Assertion is false, but Reason is true.
[Solution Description]
The Assertion states that a rolling ball stops due to gravitational force. This is incorrect because the stopping is caused by frictional force, not gravitational force. Gravitational force acts vertically downward and does not oppose horizontal motion. The Reason claims that gravitational force opposes the motion of objects in contact with the ground, which is also false since friction opposes motion, not gravity. Thus, both Assertion and Reason are false.

Key Concept: Effect of force, Push and pull, Change in motion

d) The force reverses the ball's direction without changing its speed.
[Solution Description]
The bat applies a push force to the cricket ball. The force changes the direction of the ball by 180 degrees, meaning it reverses its motion, but since the speed remains the same, only the direction is altered. This aligns with the concept that force can change the direction of a moving object without necessarily changing its speed.

Key Concept: Types of Force

c) Opening a drawer
[Solution Description]
Pulling refers to exerting force towards oneself. Among the options, opening a drawer requires pulling it outward, whereas pressing a balloon or kicking a ball involves push forces. Stretching a rubber band also involves pulling.

Key Concept: Force - Push and Pull

d) Assertion is false, but Reason is true.
[Solution Description]
The Assertion states that a force always changes the speed of an object, which is not necessarily true. A force can also change the direction or shape of an object without changing its speed. The Reason correctly defines force as a push or pull applied on an object, which is accurate. However, the Reason does not explain why the Assertion would be true because the Assertion itself is false.

Key Concept: Contact force, Muscular force, Interaction between objects

d) The forces are balanced, resulting in no movement of the cupboard.
[Solution Description]
Both children apply muscular force (a contact force) to the cupboard. Since the forces are equal and opposite, they cancel each other out, resulting in a net force of zero. Hence, the cupboard remains stationary. This demonstrates balanced forces where the interaction does not produce any motion.

Key Concept: Force as Push or Pull

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that moving a box requires a push or pull, which is correct based on the syllabus definition of force. The reason defines force as an interaction that changes motion, which is also correct and directly explains why pushing or pulling the box (applying force) moves it. Therefore, both are true, and the reason correctly explains the assertion.

Key Concept: Muscular Force

c) Lifting a box from the ground.
[Solution Description]
Muscular force is the force exerted by muscles in the body during physical activities. Among the given options, lifting a box requires contraction and elongation of muscles, making it an example of muscular force. The other options involve forces like gravitational force (apple falling) and contact force (pressing keys), but not necessarily muscular force.

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: Force effects, Multiple concepts

c) Both speed and direction change gradually
[Solution Description]
Analysis: 1) Initial rolling has kinetic energy (eastward). 2) Kick applies new force vector northward. 3) First effect: eastward motion decreases (force opposes original direction). 4) Second effect: northward motion increases. 5) Net result: direction changes northeast briefly, then north as east component vanishes. This shows multiple force effects simultaneously.

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: Effects of Force

d) Force can change the shape of an object
[Solution Description]
Applying force on an inflated balloon by pressing it changes its shape. This shows that force can alter the shape of an object when applied.

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, 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: 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

d) It changes the shape of the balloon
[Solution Description]
Applying a force on an inflated balloon, such as pressing it with hands, changes its shape temporarily. The balloon deforms due to the applied push force.

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: Changing direction and speed

c) Changes both the speed and direction of the car
[Solution Description]
The car's initial velocity ($v_i$) = 20 m/s north. Final velocity ($v_f$) = 10 m/s west. The change involves both a reduction in speed and a change in direction (from north to west). Therefore, the net effect of the force is a combination of changing speed and direction.

Key Concept: Force Changing Direction

c) The ball’s direction changes
[Solution Description]
When a moving tennis ball is hit by a racket, the force applied by the racket primarily changes the direction of the ball's motion. According to the syllabus, force can alter the direction of a moving object, as seen in the example of hitting a moving ball with a bat.

Key Concept: Balanced forces, Stopping motion

c) The braking force opposes the motion, leading to deceleration
[Solution Description]
Step 1: The cyclist is initially moving at a constant speed, meaning the forces acting on the bicycle are balanced (no acceleration).
Step 2: When brakes are applied, friction acts opposite to the direction of motion.
Step 3: This unbalanced force reduces the speed until the bicycle stops.
Hence, the braking force opposes the motion, causing deceleration and ultimately stopping the bicycle.

Key Concept: Effect of Force

b) The balloon changes its shape.
[Solution Description]
Pressing an inflated balloon applies a force that deforms the balloon, changing its shape temporarily. Once the force is removed, the balloon returns to its original shape if not burst.

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: Newton's Third Law, Interaction Forces

b) There must be another downward force of 1 N acting on the book along with its weight
[Solution Description]
According to Newton's third law, when the table exerts a 5 N force on the book, the book must exert an equal and opposite 5 N force on the table. However, the weight of the book is only 4 N, meaning there must be an additional 1 N downward force acting on the book (possibly from someone pressing down). The normal force adjusts to balance all vertical forces, so it becomes 5 N (4 N weight + 1 N applied force).

Key Concept: SI Unit of Force

c) Newton ($N$)
[Solution Description]
The SI unit of force is newton, symbolized by $N$. It represents the magnitude of force applied.

Key Concept: Action-Reaction Pairs, Non-contact Forces

a) Both magnets experience 1 N force in opposite directions
[Solution Description]
Magnetic force is an interaction between two objects following Newton's third law. Even if one magnet is stronger, the force exerted by Magnet A on Magnet B equals the force exerted by Magnet B on Magnet A. Therefore, both magnets will experience 1 N force in opposite directions, not 1.5 N or any unequal values. The action-reaction pair remains equal in magnitude.

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: Balanced forces, Net force

c) 0 N, remains at rest or moves with constant velocity
[Solution Description]
The two forces of 10 N each are applied in opposite directions. To find the net force, subtract one from the other: 10 N - 10 N = 0 N. Since the net force is zero, the box will remain at rest or continue moving at a constant velocity if it was already moving (Newton's First Law).

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: Definition of Force

c) Newton
[Solution Description]
The SI unit of force is newton, represented by the symbol $N$. This is a standard unit defined in physics.

Key Concept: Balanced and Unbalanced Forces

d) The forces acting on it are balanced
[Solution Description]
If an object is at rest, it means the net force acting on it is zero. This implies that all the forces are balanced.

Key Concept: Force Interaction, 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 book experiences two equal and opposite forces (gravitational force and normal force) resulting in no net force. This is true as the book remains at rest, indicating balanced forces. The Reason correctly states that the SI unit of force is newton ($N$) and explains that equal and opposite forces cancel each other out. The Reason provides the correct explanation for the Assertion as it links the concept of balanced forces to the observed state of the book.

Key Concept: Buoyant Force

b) 20 N
[Solution Description]
The buoyant force is the difference between the object's weight in air and its apparent weight in water. Here, the weight in air is 50 N and the weight in water is 30 N. Thus, the buoyant force is calculated as $50\,\text{N} - 30\,\text{N} = 20\,\text{N}$.

Key Concept: Force interaction, Newton's third law

d) The book exerts a force of 5 N downward on the table
[Solution Description]
According to Newton's third law, for every action, there is an equal and opposite reaction. Here, the table exerts a force of 5 N upward on the book. Therefore, the book must exert an equal and opposite force of 5 N downward on the table.

Key Concept: Force Interaction

c) The wall pushes back with equal force
[Solution Description]
According to Newton's third law, every action has an equal and opposite reaction. When the man pushes the wall, the wall exerts an equal and opposite force on the man. Since the wall doesn't move, the reaction force is equal in magnitude to the force applied by the man but in the opposite direction.

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: Forces as Interaction Between Two Objects

d) Assertion is false, but Reason is true.
[Solution Description]
The Assertion states that a force can exist without any interaction between two objects, which is false. According to Newton's Third Law of Motion, forces always occur in pairs and result from the interaction between two objects. The Reason correctly explains that forces arise only when two objects interact. Therefore, the Assertion is false, but the Reason is true.

Key Concept: Force Units and Nature

b) The unit is newton (N) and forces can act with or without contact.
[Solution Description]
The SI unit of force is the newton (N), which measures the interaction between two objects resulting in a push or pull. Forces can act through contact (like pushing a table) or at a distance (like gravity).

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: 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: Types of Forces

c) Gravitational force
[Solution Description]
Non-contact forces are those that act on objects without physical contact. Examples include gravitational force, magnetic force, and electrostatic force.

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: 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: Contact Forces

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 contact force, which is true as it requires physical interaction between objects like when we push or pull something using our muscles. The reason explains that muscular force arises from muscle contractions and elongations, which is also correct. Moreover, the reason correctly justifies why muscular force qualifies as a contact force since muscle action involves direct interaction with other objects. Therefore, both the assertion and reason are true, and the reason is the correct explanation of the assertion.

Key Concept: Contact Forces

c) Pushing a table
[Solution Description]
Contact forces act only when there is physical contact between objects. Examples include muscular force and friction. Among the options, pushing a table involves direct contact.

Key Concept: Friction, Gravitational Force

c) 2.83 m/s²
[Solution Description]
Resolve gravitational force into components:
$F_{\parallel} = mg \sin\theta = 5 \times 10 \times \sin(30°) = 25 \, \text{N}$
$F_{\perp} = mg \cos\theta = 5 \times 10 \times \cos(30°) \approx 43.3 \, \text{N}$
Frictional force opposes motion:
$F_{\text{friction}} = \mu F_{\perp} = 0.25 \times 43.3 \approx 10.825 \, \text{N}$
Net force along the incline:
$F_{\text{net}} = F_{\parallel} - F_{\text{friction}} = 25 - 10.825 = 14.175 \, \text{N}$
Acceleration:
$a = \frac{F_{\text{net}}}{m} = \frac{14.175}{5} \approx 2.835 \, \text{m/s}^2$
Closest option is 2.83 m/s².

Key Concept: Muscular Force Examples

c) Lifting a heavy box
[Solution Description]
Activities like lifting, pushing, or chewing involve muscular force because they require the contraction and elongation of muscles. Non-physical forces like gravitational pull do not involve 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

c) It moves food through the gut.
[Solution Description]
During digestion, muscular force helps in chewing food and moving it through the alimentary canal via peristalsis, which involves rhythmic muscle contractions.

Key Concept: Muscular force, Internal body functions

c) Pumping of blood by the heart
[Solution Description]
Muscular force plays a crucial role in internal body functions such as blood circulation. The heart muscles contract and relax rhythmically to pump blood throughout the body, ensuring oxygen and nutrients are delivered to tissues. This process is essential for survival.

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: Basic Concept: Direction of Friction

c) Opposite to the motion
[Solution Description]
Friction always acts in a direction opposite to the direction in which the object is moving or trying to move.

Key Concept: Direction of Frictional Force

c) Opposite to the direction of motion.
[Solution Description]
Frictional force always opposes the relative motion between two surfaces in contact. When a book slides across a table, the frictional force acts opposite to the direction of the book's motion.

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: Gravitational Force

c) Gravitational force
[Solution Description]
Gravitational force is the non-contact force exerted by the Earth that attracts objects towards its center. This is why a ball thrown upwards eventually falls back to the ground.

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: Magnetic Force

c) The force exerted by a magnet on another magnet
[Solution Description]
Magnetic force is a type of non-contact force, as it can act without direct contact between objects, such as when two magnets repel or attract each other. Among the given options, magnetic force fits this description.

Key Concept: Magnetic Force - Pole interaction

c) The second magnet will be pulled downward
[Solution Description]
When unlike poles (North-South) of magnets face each other, they attract. Thus, the second magnet will not remain floating but will be pulled towards the first magnet.

Key Concept: Non-contact force

b) Magnetic force
[Solution Description]
Magnetic force is a non-contact force because it can act over a distance without requiring physical contact between the objects.

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 - 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

b) The paper pieces are attracted to the balloon.
[Solution Description]
When a negatively charged balloon is brought close to uncharged paper pieces, the negative charge on the balloon induces a temporary separation of charges in the paper (polarization). The positive charges in the paper are attracted towards the balloon while the negative charges are repelled. Since the force of attraction between the balloon and the closer positive charges is stronger than the repulsion from the farther negative charges, the paper pieces are pulled towards the balloon.

Key Concept: Electrostatic Force: Repulsion

b) They repel each other.
[Solution Description]
According to the principle of electrostatics, like charges repel each other. Since both balloons have the same type of charge (positive), they will exert a repulsive force on each other and move away.

Key Concept: Electrostatic force: Force between charged objects

c) Assertion is true, but Reason is false.
[Solution Description]
The assertion states that when two balloons are rubbed with a woollen cloth and released, they repel each other. This is true because rubbing the balloons transfers electrons, making them similarly charged. According to Coulomb's Law ($F = k \frac{q_1 q_2}{r^2}$), like charges repel each other. However, the reason given is "Like charges attract each other," which is false because like charges repel, not attract. Therefore, the assertion is true, but the reason is false.

Key Concept: Types of Charges

b) Positive and Negative
[Solution Description]
The two kinds of static charges are positive and negative. This classification explains why like charges repel and unlike charges attract.

Key Concept: 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 the Moon's gravity is about 1/6th of Earth's gravity. The Reason correctly explains this by stating that the Moon exerts a weaker gravitational force compared to Earth. Therefore, both the Assertion and Reason are true, and the Reason correctly explains the Assertion.

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 and Weight

c) 8 N
[Solution Description]

Key Concept: Weight on Different Planets

c) 1.6 N
[Solution Description]
From the syllabus table, the weight of a 1 kg object on the Moon is 1.6 N compared to 10 N on Earth. Therefore, if an object weighs 10 N on Earth, it will weigh approximately $\frac{1.6}{10} \times 10 = 1.6$ N on the Moon.

Key Concept: Spring Balance

b) 700 g
[Solution Description]
To find the mass of the object:
1. Given that the weight of the object is $7 N$.
2. Use the formula $\text{Mass} = \frac{\text{Weight}}{\text{Gravity}} = \frac{7 N}{10 N/kg} = 0.7 kg = 700 g$.

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 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: 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: Comparative weights, unit conversion

c) 2.54 times
[Solution Description]
On Earth: Weight = $5 kg \times 10 N/kg = 50 N$
On Jupiter: Weight = $5 kg \times 25.4 N/kg = 127 N$
Increase factor:
$\frac{127 N}{50 N} = 2.54$

Key Concept: Weight and Its Measurement

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that weight is measured in newtons (N), which is true because weight is a force, and its SI unit is newton. The reason states that weight is the force with which the Earth pulls an object towards itself, which is also true. Moreover, the reason correctly explains why weight is measured in newtons (N) as it defines weight as a force, and force is measured in newtons.

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: Gravitational Force Calculation

b) 49 N
[Solution Description]
Weight can be calculated using the formula $F_g = m \times g$, where $m$ is mass and $g$ is acceleration due to gravity. Substituting the values: $F_g = 5\,kg \times 9.8\,m/s^2 = 49\,N$.

Key Concept: Difference between weight and mass

d) Assertion is false, but Reason is true.
[Solution Description]
The assertion states that the weight of an object is the same on Earth and the Moon. This is false because weight varies with gravitational force, which is different on Earth and the Moon. The reason states that mass is the amount of matter in an object, while weight depends on gravity, which is true and correctly explains why the assertion is false. Therefore, the correct option is d).

Key Concept: Weight Variation on Different Planets

b) 1.6 N
[Solution Description]
The weight of an object on the Moon is $\frac{1}{6}$ of its weight on Earth. Thus:
$10\,N \times \frac{1.6\,N}{10\,N} = 1.6\,N$

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 the weight of an object changes on different planets. This is true because weight depends on the gravitational force acting on the object, which varies from planet to planet (e.g., Earth's gravity is stronger than the Moon's).
The reason states that the mass remains constant while gravitational force changes. This is also correct because mass is independent of location, whereas weight ($W = m \times g$) depends on both mass ($m$) and gravitational acceleration ($g$), which differs for each planet. Moreover, the reason correctly explains why the assertion is true—since $g$ changes, weight changes even if mass stays the same.
Therefore, both the assertion and reason are true, and the reason is the correct explanation of the assertion.

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: Spring Balance Smallest Division

b) 0.2 N
[Solution Description]
The smallest weight measurable is the value of one small division. Since 5 small divisions make up 1 N, each small division represents $\frac{1\ \text{N}}{5} = 0.2\ \text{N}$.

Key Concept: Measurement of weight using a spring balance

b) 367 g
[Solution Description]
Weight ($W$) is related to mass ($m$) by the formula $W = mg$. Rearranged for mass, $m = \frac{W}{g}$. Substituting the values, $m = \frac{3.6 \, \text{N}}{9.8 \, \text{m/s}^2} \approx 0.367 \, \text{kg}$. To convert kg to grams, multiply by 1000: $0.367 \times 1000 = 367 \, \text{g}$.

Key Concept: Weight measurement using spring balance

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
Weight is the force with which a celestial body attracts an object, given by $W = mg$, where $m$ is mass and $g$ is gravitational acceleration. On the Moon, $g$ is about $\frac{1}{6}$ of Earth's $g$. Thus, for the same mass, weight on the Moon is less than on Earth. The assertion states that readings differ on Earth and Moon, which is true as weight depends on $g$. The reason correctly explains this relationship between weight and gravitational acceleration. Hence, both are true, and the reason is the correct explanation.

Key Concept: Spring balance operation, weight measurement

c) 4.76 N
[Solution Description]
Difference between 4.6 N and 4.8 N = 0.2 N. With 5 divisions, each represents $\frac{0.2 N}{5} = 0.04 N$. The pointer is closest to 4.8 N minus one division (since it's below 4.8 N), so reading = $4.8 N - 0.04 N = 4.76 N$.

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: Buoyant Force and Floating Condition

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that a wooden block floats on water because the buoyant force equals its weight, which is true. The reason states Archimedes' principle correctly: an object floats when the weight of the displaced liquid equals the weight of the object. Since the reason accurately explains why the assertion is true, both are correct and the reason justifies the assertion.

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: 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: Buoyant force, Floating condition

b) 20%
[Solution Description]
First, find the volume of the block: $V = \frac{m}{\rho_s} = \frac{2}{800} = 0.0025$ m$^3$.
When floating, the buoyant force equals the block's weight: $\rho_l \cdot V_{\text{submerged}} \cdot g = m \cdot g$.
Substituting values: $1000 \cdot V_{\text{submerged}} = 2$.
Thus, $V_{\text{submerged}} = 0.002$ m$^3$.
The fraction submerged is $\frac{V_{\text{submerged}}}{V} = \frac{0.002}{0.0025} = 0.8$.
Therefore, the fraction above water is $1 - 0.8 = 0.2$ or 20%.

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: 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: Upthrust or buoyant force

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The Assertion is true because the buoyant force reduces the apparent weight of the submerged mug, making it feel lighter. The Reason is also true as it correctly explains the cause of the buoyant force according to Archimedes' Principle, which states that the buoyant force equals the weight of the displaced liquid. Therefore, both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

Key Concept: Archimedes' Principle

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that a plastic bottle with a tightly closed lid floats on water. According to Archimedes' Principle, an object floats if the buoyant force ($F_b$) equals the weight of the displaced fluid. When the lid is closed tightly, air is trapped inside the bottle, increasing its overall volume and decreasing its average density. This makes the buoyant force equal to the weight of the displaced water, causing the bottle to float. Therefore, both the assertion and reason are true, and the reason correctly explains the assertion.

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: 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.

Key Concept: Floating Condition

b) Sink because the weight exceeds the buoyant force
[Solution Description]
According to Archimedes’ Principle, an object will float if its weight is less than or equal to the buoyant force (weight of displaced fluid). Here, the object's weight (500 N) is greater than the buoyant force (400 N). Thus, the object will sink.