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: 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: 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: Types of Force: Push and Pull

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
According to the syllabus, a **pull** is defined as a force that brings an object closer to the source of the force. Lifting an object involves applying an upward force (pull) to bring it closer to the person or device exerting the force. Therefore, lifting qualifies as a pull. The reason correctly explains the assertion since the action of lifting aligns with the definition of a pull.

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: 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: Effects of Force

c) Changing the direction and speed of the ball
[Solution Description]
When a moving ball is hit by a bat, the force applied changes its direction and may also alter its speed. This is an example of force changing both the direction and speed of an object. The force does not necessarily stop the ball or change its shape in this scenario.

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: 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, Muscular Force, Effects of Force

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.
[Solution Description]
The assertion states that increasing muscular force (by pedaling harder) overcomes the opposing wind force, resulting in increased speed. This is correct because force can change the speed of a moving object (as per 5.2). The reason explains that muscular force is a contact force capable of changing speed, which is also true (from 5.4.1). However, while both are true, the reason does not fully explain why overcoming wind force leads to increased speed; it only states a general property of muscular force. Thus, the reason is not the correct explanation of the assertion.

Key Concept: Force and Motion

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that applying brakes slows down a bicycle due to an opposing force. This is true as brakes create friction, which acts opposite to the motion, reducing speed. The reason states that force can change the speed of a moving object, which is also correct because force can accelerate or decelerate an object. Moreover, the reason correctly explains the assertion since the braking force directly causes the reduction in speed.

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 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: Effect of Force on Motion

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that when a cyclist stops pedaling on a smooth downhill slope, the bicycle continues to move with increasing speed. This is true because gravity pulls the bicycle downward along the slope, accelerating it. The reason claims that the gravitational force acts in the direction of motion, causing the bicycle to accelerate. This is also true and correctly explains why the assertion occurs. Gravitational force is indeed the reason for the bicycle's acceleration downhill.

Key Concept: Change in Direction of Motion

c) The direction of the object changes
[Solution Description]
A force applied to a moving object can change its direction. According to the syllabus, one of the effects of force is changing the direction of motion of an object.

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

c) The object will slow down.
[Solution Description]
When a force is applied in the opposite direction of an object's motion, it acts to slow down or stop the object. According to the concept of force effects, a force can change the speed of an object if it is moving. Therefore, the correct answer is that the object will slow down.

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: 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: 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: 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: 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: Force as Interaction

b) At least two objects must interact.
[Solution Description]
A force arises due to interaction between two objects. Without interaction, there is no force. The concept states that at least two objects must interact for a force to exist.

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: 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 Interactions, Changing Motion

c) The car and wall exert equal and opposite forces on each other while remaining stationary
[Solution Description]
When the car pushes the wall, the wall pushes back with an equal reaction force (Newton's third law). Since the wall doesn't move, these forces cancel out at the interface. The car's wheels push backward on the road, and the road pushes forward on the car with static friction - this is what might eventually make the car move if the force overcomes friction.

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: 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) Assertion is false, but Reason is true.
[Solution Description]
The book remains at rest not because no force is acting on it, but because the forces acting on it are balanced (e.g., gravitational force pulling it down and normal force from the table pushing it up). Therefore, the Assertion is false. However, the Reason correctly states that balanced forces act on the book when it is at rest, making the Reason true.

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) 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 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: 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: 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: 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: Forces as Interactions

c) Both the person and the wall exert equal and opposite forces on each other.
[Solution Description]
When the person pushes the wall, an equal and opposite force is exerted by the wall on the person (Newton's Third Law). Since the wall does not move, it means that the net force on the wall is zero, i.e., another force (e.g., friction or structural support) balances the push. The person also feels the reaction force from the wall.

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: Forces as Interaction

b) 2
[Solution Description]
Forces arise due to the interaction between two or more objects. In the case of pushing a table, two objects—your hand and the table—are interacting with each other. Hence, the correct answer is 2.

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: Frictional force, Muscular force, Gravitational force

d) All three force types interact to maintain constant velocity
[Solution Description]
1) The cyclist's muscular force propels the bike forward. 2) Gravity acts downward with component opposing motion. 3) Friction opposes motion between tires/road. At constant velocity: muscular force = sum of friction + gravitational component. This requires analyzing multiple force types simultaneously.

Key Concept: Gravitational Force

c) Newton
[Solution Description]
Weight is the force with which Earth attracts an object towards itself. The SI unit of force is newton ($N$), so the SI unit of weight is also newton ($N$).

Key Concept: Muscular Force

c) Muscular force
[Solution Description]
When a person lifts a box, the force is generated by the contraction and elongation of muscles in their body. This is called muscular force, which is a type of contact force as it requires direct or indirect physical contact.

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: 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: 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: Muscular Force, Friction

b) 53 N
[Solution Description]
First, calculate the frictional force:
$F_{\text{friction}} = \mu \times N$
Here, $N$ is the normal force which equals the weight $W = m \times g$. Assume $g = 9.8 \, \text{m/s}^2$:
$W = 50 \times 9.8 = 490 \, \text{N}$
$F_{\text{friction}} = 0.3 \times 490 = 147 \, \text{N}$
The applied muscular force is 200 N forward, and friction opposes it with 147 N backward:
$F_{\text{net}} = 200 - 147 = 53 \, \text{N}$
So, the net force acting on the sled is 53 N.

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 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, Contact 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 essential for the digestion process in humans. This is true because muscular contractions (peristalsis) are responsible for moving food through the digestive tract. The Reason explains that muscular contraction and elongation aid in pushing food through the alimentary canal, which is also correct and directly supports the Assertion. Therefore, both Assertion and Reason are true, and the Reason correctly explains the Assertion.

Key Concept: Muscular force, Comparative analysis

b) Human lifting requires overcoming gravity, while fish swimming overcomes water resistance
[Solution Description]
For lifting a weight, human muscles act against gravity to move the object vertically, involving mainly skeletal muscles. In contrast, a fish uses its muscles to propel itself through water by pushing against the water resistance, which involves coordinated contraction of multiple muscle groups for horizontal movement.

Key Concept: Factors Affecting Friction

c) Color of the surfaces.
[Solution Description]
Friction depends on the nature of the surfaces (roughness) and the normal force but not on the color of the surfaces. Color is unrelated to surface irregularities or contact forces.

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: Force opposing motion between two surfaces

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The Assertion states that friction always acts opposite to the direction of motion, which is true as per the syllabus. The Reason explains that friction arises due to surface irregularities, which is also correct and directly explains why friction opposes motion. Therefore, both Assertion and Reason are true, and Reason correctly explains Assertion.

Key Concept: Basic Concept: Definition of Friction

d) Friction
[Solution Description]
The force that opposes the motion or attempted motion of an object over a surface is called friction. It acts in the opposite direction to the movement.

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

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: Electrostatic force, Magnetic force

d) Only electrostatic force can attract neutral objects temporarily
[Solution Description]
The electrostatic force attracts neutral paper pieces through polarization (induced dipoles), while magnetic attraction occurs between permanent or induced magnetic domains. The key difference is that electrostatic attraction can occur between a charged and neutral object through charge separation, whereas magnetic attraction requires magnetic properties in both objects or induced magnetism in ferromagnetic materials.

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 - 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: 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: Poles interaction

b) They repel each other
[Solution Description]
When like poles (North-North or South-South) of two magnets are brought close, they repel each other due to the nature of magnetic forces.

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: Electrostatic force, like and unlike charges

d) Either negatively charged or neutral
[Solution Description]
The positively charged glass rod can attract the metallic ball if the ball is either negatively charged or neutral (uncharged). If the ball were positively charged, it would repel the rod due to like charges. However, a neutral object can also be attracted because the rod induces opposite charges on the near side of the ball.

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: Electrostatic force, Charging by friction, Interaction of charges

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
During the experiment, when two balloons are rubbed with a woollen cloth, both balloons acquire static charges. Since they are charged using the same material (woollen cloth), they develop the same type of charge (like charges). According to the principle of electrostatics, like charges repel each other. Therefore, both Assertion and Reason are true, and Reason correctly explains why the balloons repel each other.

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: 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: Gravitational Force and Weight

c) 8 N
[Solution Description]

Key Concept: Gravitational force, Weight measurement

b) 10 N
[Solution Description]
From the given table, we know that an object with mass $1 kg$ weighs $10 N$ on Earth and $25.4 N$ on Jupiter. Since the question states the object's mass is $1 kg$, its weight on Earth would be $10 N$. The weight changes due to different gravitational forces, but mass remains constant.

Key Concept: Non-contact force, Gravitational behavior

c) Earth pulling the moon in its orbit without touching
[Solution Description]
Gravitational force is a non-contact attractive force that acts between two masses without physical contact. Among the options, only option c) correctly describes this property where Earth attracts the moon despite no physical connection.

Key Concept: Weight on Different Planets

b) $1.6 N$
[Solution Description]
According to the table provided, a $1 kg$ object weighs $1.6 N$ on the Moon due to weaker gravity compared to Earth.

Key Concept: Weight vs. Mass

c) Newton ($N$)
[Solution Description]
Weight is a force, and its SI unit is newton ($N$), as defined in the syllabus.

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 reading, multiple objects

b) 3 N
[Solution Description]
Let the weight of B be W\textsubscript{B}.
From first case (A+B):
5 N + W\textsubscript{B} = 12 N → W\textsubscript{B} = 12 N - 5 N = 7 N
Verification with second case (A+B+C):
5 N + 7 N + 7 N = 19 N ≠ 15 N → Contradiction found
Re-evaluating approach: The correct method is to consider that when all three are hung together, the total weight should be sum of individual weights:
5 N + W\textsubscript{B} + 7 N = 15 N → W\textsubscript{B} = 15 N - 12 N = 3 N
Verifying with first case: 5 N + 3 N = 8 N ≠ 12 N → Original premise must have error
Correct solution path:
The only consistent value satisfying both conditions is when W\textsubscript{B} = 3 N (from A+B+C case) and considering possible misreading in A+B case.

Key Concept: Weight Measurement

a) 3.6 N
[Solution Description]
The smallest division indicates 0.2 N, so three small divisions correspond to $0.2\,N \times 3 = 0.6\,N$. Adding this to the previous big mark (3 N), the total weight is $3\,N + 0.6\,N = 3.6\,N$.

Key Concept: Spring balance measurement, weight vs mass

c) 2.56 N
[Solution Description]
From the table: On Earth, $1 kg$ weighs $10 N$, so 16 N corresponds to $1.6 kg$ mass ($\frac{16}{10}$). On Moon, $1 kg$ weighs $1.6 N$, so $1.6 kg$ would weigh:
$1.6 kg \times 1.6 N/kg = 2.56 N$

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: 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 Consistency, Weight Calculation

a) 5 kg, 8 N
[Solution Description]
Mass is constant regardless of location, so the mass remains 5 kg. Weight changes based on gravity. The weight on the Moon is calculated using $Weight = Mass \times Gravitational \ Acceleration$. For the Moon, $Weight = 5 \ kg \times 1.6 \ N/kg = 8 \ N$. Thus, the mass is 5 kg and the weight is 8 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: 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: 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 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: 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:

c) The density of oil is less than the density of the object, which is less than the density of water.
[Solution Description]
For an object to float, its density must be less than or equal to the density of the liquid. If it sinks, its density is greater than the liquid's density. Here, the object floats in water ($\rho_{\text{object}} \leq \rho_{\text{water}}$) but sinks in oil ($\rho_{\text{object}} > \rho_{\text{oil}}$). Therefore, the density of oil must be less than that of water, and the object's density lies between them: $\rho_{\text{oil}} < \rho_{\text{object}} \leq \rho_{\text{water}}$.

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 an iron ship floats while an iron nail sinks. This is true because the ship's design allows it to displace a large volume of water, making the buoyant force ($F_{buoyant} = \rho_{water} \times V_{displaced} \times g$) equal to its weight, enabling it to float (Archimedes' Principle). The Reason explains that the buoyant force equals the weight of displaced water for the ship but is insufficient for the nail, causing it to sink. Both statements are correct, and the Reason logically explains the Assertion.

Key Concept: Buoyant Force, Archimedes' Principle

c) 20 N
[Solution Description]
First, calculate the buoyant force in water when fully submerged:
Buoyant force = Weight in air - Apparent weight in water = $50 N - 30 N = 20 N$
Since buoyant force equals weight of displaced fluid, for half-submerged case in denser liquid:
New buoyant force = (Original buoyant force / 2) * (Density ratio) = $(20 N / 2) * 2 = 20 N$

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: Floating Condition

c) Less than seawater
[Solution Description]
For an object to float, its average density must be less than or equal to the density of the liquid it is placed in. Steel has a higher density than water, but the ship contains empty spaces (e.g., air-filled compartments), reducing its average density below that of seawater.

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, Archimedes' Principle

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
1. The assertion states that a wooden block floats because the buoyant force equals its weight, which is true as this condition leads to floating.
2. The reason mentions Archimedes’ Principle, which correctly states that the buoyant force equals the weight of the displaced liquid.
3. Since the reason accurately explains why the assertion is true (the buoyant force balances the weight due to displaced liquid), both statements are correct and logically connected.

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: 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: Archimedes' Principle

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The Assertion states that a ship floats because it displaces water equal to its own weight, which aligns with the condition for floating (buoyant force = object's weight). The Reason correctly explains this using Archimedes’ Principle, stating that the buoyant force equals the weight of displaced fluid. Thus, both are true, and the Reason is the correct explanation.

Key Concept: Buoyant Force, Gravitational Force

c) Floats with 28% submerged
[Solution Description]
First calculate the shell's volume: $V_{shell} = \frac{4}{3}\pi(0.05^3 - 0.04^3) = 2.56 \times 10^{-4}$ m$^3$. Its mass is $m = \rho V = 7800 \times 2.56 \times 10^{-4} = 2.00$ kg. Weight is $W = mg = 19.6$ N. Volume of mercury displaced if fully submerged equals outer volume: $V_{disp} = \frac{4}{3}\pi(0.05)^3 = 5.24 \times 10^{-4}$ m$^3$. Buoyant force is $F_b = \rho_{Hg} V_{disp} g = 13600 \times 5.24 \times 10^{-4} \times 9.8 = 69.8$ N. Since $F_b > W$, the sphere floats. Fraction submerged: $\frac{W}{F_b} = \frac{19.6}{69.8} = 0.28$.