Key Concept: Force, Change in Shape

c) The rubber band will stretch unevenly, changing its shape.
[Solution Description]
The question deals with the effect of unbalanced forces on an object's shape. Initially, balanced forces ($5 \, \text{N}$ each) stretch the rubber band uniformly. When one force increases to $10 \, \text{N}$, the net force becomes $5 \, \text{N}$ ($10 - 5 = 5$) in the direction of the larger force. This unbalanced force will further stretch the rubber band unevenly, leading to a change in shape.
Step-by-step reasoning:
1. Initially, both forces are $5 \, \text{N}$, resulting in no net force and uniform stretching.
2. Increasing one force to $10 \, \text{N}$ creates a net force of $5 \, \text{N}$.
3. The rubber band will stretch more on the side with the larger force, altering its 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: 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: 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: Force Interaction

c) An interaction between the objects
[Solution Description]
For a force to act between two objects, there must be an interaction between them, whether through direct contact (contact force) or without contact (non-contact force). Physical contact is necessary only for contact forces, but interaction is essential for any force to act.

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: 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 interaction, Muscular force, Type of force

d) Both the boy and the box move towards each other.
[Solution Description]
When the boy pulls the rope, he applies a muscular force (a contact force) to the rope, which then transmits this force to the box. According to Newton's Third Law, the box also exerts an equal and opposite force on the boy through the rope. Since there is no friction, both the boy and the box will move towards each other due to these opposing forces.

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: 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: 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: 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) 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: 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: Force, Balanced Forces, State of Motion

d) The forces acting on the object are balanced.
[Solution Description]
An object remains at rest when the net force acting on it is zero. This means that all the forces acting on the object are balanced. In this case, the gravitational force pulling the object downward is balanced by the normal force exerted by the table upward. According to Newton's first law of motion, an object at rest stays at rest unless acted upon by an unbalanced force.

Key Concept: Types of Forces

c) Muscular force
[Solution Description]
The act of lifting involves muscular force, which is exerted by living beings using their muscles. In this case, the child uses muscular force to lift the school bag.

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

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: Changing speed and direction

d) \(4\,\mathrm{m\,s^{-2}}\ \text{westward}\)
[Solution Description]
First, we calculate the change in velocity. Initial velocity ($v_i$) = 5 m/s eastward. Final velocity ($v_f$) = 3 m/s westward. Since they are opposite directions, we take westward as negative and eastward as positive.
Change in velocity ($\Delta v$) = $v_f - v_i$ = $-3 - 5 = -8$ m/s (westward).
Time taken ($t$) = 2 s.
Average acceleration \[
a=\frac{\Delta v}{t}=\frac{-8\ \mathrm{m/s}}{2\ \mathrm{s}}=-4\ \mathrm{m/s^2}
\]
The negative sign indicates the direction is westward.

Key Concept: Force and Direction Change

c) It changes the direction of the ball's motion.
[Solution Description]
When a force is applied to a moving object at an angle, it can change the direction of the object's motion. Hitting the cricket ball with a bat applies a force that alters its path, demonstrating a directional change as per the syllabus examples. This effect is distinct from changing speed, shape, or bringing the ball to rest.

Key Concept: Effects of Force

d) The ball stops moving
[Solution Description]
When a fielder catches a moving cricket ball, they apply a force to stop the ball's motion. According to the concepts discussed, a force can change the speed or direction of a moving object or bring it to rest. Here, the ball was initially in motion, and the fielder's action stops it completely. Therefore, the effect is stopping or decreasing the speed of the ball.

Key Concept: Change in Shape Due to Force

b) Stretching a rubber band
[Solution Description]
From the given syllabus examples, pressing an inflated balloon causes a change in its shape. This occurs because the applied force deforms the elastic material of the balloon temporarily. Thus, this situation clearly illustrates how force can alter the shape of an object.

Key Concept: Effect of force, Change in shape

c) The rubber band changes its shape but does not accelerate
[Solution Description]
Step 1: The rubber band is subjected to two equal and opposite forces (10 N each).
Step 2: Since the forces are balanced (net force is zero), there is no change in the state of motion of the rubber band.
Step 3: However, the rubber band stretches because the applied forces cause its shape to change.
Thus, the primary effect here is a change in shape without any net acceleration.

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: Unit of Force

d) Newton, symbol $N$
[Solution Description]
The SI unit of force is newton, named after Sir Isaac Newton, and its symbol is $N$. It is used to measure the magnitude of force.

Key Concept: Forces as Interaction

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that a force cannot exist if only one object is present, which is true because forces require interaction between two or more objects, as mentioned in the syllabus. The reason correctly explains why the assertion is true: forces arise due to interaction between at least two objects. Thus, both are true, and the reason correctly explains the assertion.

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 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: Interaction forces, Action-reaction pairs

d) The wall exerts an equal and opposite force back on the person
[Solution Description]
According to Newton's Third Law, when the person exerts a 50 N force on the wall, the wall exerts an equal and opposite force of 50 N back on the person. These forces act on different objects (one on the wall and one on the person) and form an action-reaction pair.

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: 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: Balanced and Unbalanced Forces

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that an object moving with constant velocity must be experiencing balanced forces. This is true because when forces are balanced, there is no net force acting on the object, resulting in no acceleration (constant velocity or at rest). The reason states that balanced forces result in no change in the state of motion of an object, which is also true and correctly explains why the assertion is true. Therefore, both the assertion and reason are true, and the reason is the correct explanation of the assertion.

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: 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 interaction, Balanced forces

d) All forces acting on the car are balanced
[Solution Description]
When an object moves with constant velocity, the net force acting on it is zero. This means all the forces acting on the car are balanced - i.e., the driving force equals the opposing frictional forces.

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 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: Force 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 to prevent it from falling. This is true because the book exerts a gravitational force (weight) on the table, and the table reacts by exerting a normal force upward, balancing the book's weight. The reason states Newton's Third Law, which explains that forces always occur in pairs (action-reaction pairs). Here, the reason correctly explains the assertion since the interaction between the book and the table follows Newton's Third Law. Thus, both assertion and reason are true, and the reason explains the assertion correctly.

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 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: 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: 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

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: Contact and Non-Contact Forces

c) Magnetic force
[Solution Description]
Non-contact forces are those that act between objects without any physical contact. Examples include magnetic force, electrostatic force, and gravitational force. Muscular force is a contact force, while frictional force also requires contact.

Key Concept: Muscular Force and Friction

c) The ball slows down and stops due to frictional force
[Solution Description]
The ball gradually slows down and stops due to the force of friction. Friction opposes the motion of the ball when it moves across the surface.

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: Friction

c) It slows down and stops due to friction
[Solution Description]
Friction acts opposite to the direction of motion, slowing down the bicycle. When pedaling stops, friction causes the bicycle to decelerate and eventually come to rest.

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

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: 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 Applications

c) By contracting and relaxing muscles to move food
[Solution Description]
Muscular force helps in digestion by contracting and relaxing muscles to chew food and push it through the alimentary canal. This mechanical process aids in breaking down food for nutrient absorption.

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: 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: 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, 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: 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: 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 second magnet floats above the first magnet without touching it.
[Solution Description]
When two magnets have their like poles facing each other, they repel each other due to magnetic force. This is a non-contact force, so the second magnet will float above the first one without physical contact.

Key Concept: Electrostatic Force

d) The paper pieces are attracted toward the plastic scale.
[Solution Description]
Rubbing the plastic scale with polythene builds up static charges on the scale. These charged objects exert an electrostatic force on neutral objects like paper pieces, attracting them without physical contact.

Key Concept: Non-contact Forces

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The Assertion states that a magnet can attract iron nails without touching them, which is true as magnetic force acts at a distance. The Reason claims that magnetic force is a non-contact force acting between magnets and magnetic materials, which is also true. Additionally, the Reason correctly explains why the Assertion is valid since the non-contact nature of magnetic force allows attraction without physical contact. Hence, both are true, and the Reason is the correct explanation.

Key Concept: Magnetic Force

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that when two magnets are placed with like poles facing each other, they repel each other. This is true because according to the properties of magnetic forces, like poles (North-North or South-South) repel each other. The reason given is that like poles of magnets exert a non-contact repulsive force on each other, which is also true and correctly explains why the assertion is correct. Magnetic force is indeed a non-contact force, and it follows the rule that like poles repel.

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: 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 - 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: 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 - 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, 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: 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: 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: Weight Unit

b) Newton
[Solution Description]
Weight, being a force, is measured in newtons ($N$). This is part of the International System of Units (SI).

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 and Weight

c) 8 N
[Solution Description]

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: 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, which is correct because weight is a type of force (gravitational force) and the SI unit of force is newton (N). The Reason explains this correctly by mentioning that weight is the gravitational force acting on an object, and force is indeed measured in newtons. Therefore, both the Assertion and Reason are true, and the Reason correctly explains the Assertion.

Key Concept: Gravitational Force Comparison

b) 1.89 N
[Solution Description]
To find the weight on the Moon:
1. Calculate the mass of the object using Jupiter's gravity: $\text{Mass} = \frac{30 N}{25.4 N/kg} \approx 1.18 kg$.
2. Now compute the weight on the Moon: $1.18 kg \times 1.6 N/kg \approx 1.89 N$.

Key Concept: Weight vs. Mass

b) 19 N
[Solution Description]
To find the weight of the object on Mars:
1. First, calculate the weight per kilogram on Mars: Given that $1 kg$ weighs $3.8 N$.
2. Multiply the mass by the weight per kilogram on Mars: $5 kg \times 3.8 N/kg = 19 N$.

Key Concept: Spring Balance Measurement

c) Weight of the object in newtons
[Solution Description]
A spring balance measures the gravitational force (weight) acting on an object. The reading directly indicates the weight in newtons (N).

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: 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: 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: 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: 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: Difference between weight and mass, Gravitational force variation

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 Moon's weaker gravitational pull. This is true because weight depends on the gravitational force, which varies with location. The reason given is that the mass of an object remains constant regardless of its location, which is also true as mass is an intrinsic property of matter. However, the reason does not directly explain why the weight changes; it merely states a fact about mass. Therefore, both statements are true, but the reason is not the correct explanation for the assertion.

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: 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: 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 Maximum Weight

b) 10 N
[Solution Description]
The maximum weight a spring balance can measure is given by its upper limit, which is explicitly stated as 10 N.

Key Concept: Measurement of weight using a spring balance

b) 24
[Solution Description]
The total weight is 4.8 N, and each small division represents 0.2 N. The number of small divisions moved is calculated as $\frac{4.8 \, \text{N}}{0.2 \, \text{N}} = 24$.

Key Concept: Volume Displacement, Multiple Fluids

c) $\rho_s = 0.4\rho_1 + 0.5\rho_2$
[Solution Description]
Using Archimedes' principle for equilibrium:
Weight of sphere = Total buoyant force
$\rho_s V g = \rho_1 (0.4V) g + \rho_2 (0.5V) g$
Cancel $Vg$ from all terms:
$\rho_s = 0.4\rho_1 + 0.5\rho_2$
Remaining 10% is above the interface

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 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:

b) $w_3 > w_2 > w_1$
[Solution Description]
According to Archimedes’ principle, for floating ($w_1$), the object's weight equals the weight of displaced water. For suspended ($w_2$), the object's weight exactly balances the buoyant force (fully submerged but neither sinks nor rises). For sinking ($w_3$), the object's weight exceeds the buoyant force. Since all have the same volume, the buoyant force is the same when fully submerged. Thus:
$w_1 < w_2 = \text{Buoyant Force} < w_3$

Key Concept: Buoyant force, Density, Archimedes' Principle

c) $\rho_s = \frac{\rho_l}{2}$
[Solution Description]
According to Archimedes' Principle, the buoyant force equals the weight of the displaced liquid. The weight of the displaced liquid is $\rho_l \cdot \frac{V}{2} \cdot g$, and the weight of the sphere is $\rho_s \cdot V \cdot g$. For the sphere to float, these must be equal:
$\rho_s \cdot V \cdot g = \rho_l \cdot \frac{V}{2} \cdot g$
Simplifying, we get:
$\rho_s = \frac{\rho_l}{2}$
Hence, the density of the sphere is half the density of the liquid.

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: Buoyant Force and Archimedes' Principle

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 because the buoyant force equals its weight, which is correct. This condition is necessary for floating as per the equilibrium principle. The reason correctly cites Archimedes' Principle, which states that the buoyant force equals the weight of the displaced liquid, explaining why the assertion holds true. Therefore, both are true, and the reason correctly explains the assertion.

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

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: Buoyant Force Calculation

c) 200 N
[Solution Description]
The buoyant force is calculated using Archimedes’ Principle:
$\text{Buoyant Force} = \text{Weight of displaced fluid}.$
First, find the mass of the displaced water:
$\text{Mass} = \text{Density} \times \text{Volume} = 1000 \text{ kg/m}^3 \times 0.02 \text{ m}^3 = 20 \text{ kg}.$
Now, calculate the weight of the displaced water:
$\text{Weight} = \text{Mass} \times g = 20 \text{ kg} \times 10 \text{ m/s}^2 = 200 \text{ N}.$
Therefore, the buoyant force is 200 N.

Key Concept: Archimedes' Principle

c) Weight of the displaced fluid
[Solution Description]
Archimedes' principle states that the buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object. The formula is $F_{\text{buoyant}} = W_{\text{displaced}}$. This means the upward force experienced by the object is exactly the weight of the liquid it pushes aside.

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.