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: 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: Effects of Force

c) Increasing the mass of an object
[Solution Description]
Force can make an object move from rest, change its speed or direction, or alter its shape. However, force does not directly increase the mass of an object.

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: 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: 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: 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: 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: 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: 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 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 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: Force, Change in Motion, Direction

c) The ball continues at the same speed but changes direction.
[Solution Description]
The ball is initially moving horizontally at a constant speed. When a force is applied perpendicular to its motion, it does not affect the speed but changes the direction of motion. According to the concept of force, a force can change the direction of an object's motion without necessarily altering its speed. Thus, the ball will continue moving but in a changed direction.

Key Concept: Force and its Effects

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

Key Concept: Effects of Force on Objects

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

Key Concept: Force, 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: 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: 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 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: Effect of force on motion and shape

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

Key Concept: Effects of Force on Objects

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

Key Concept: 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: 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 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: 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: 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: 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: 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 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

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

Key Concept: Unbalanced forces, Acceleration

b) \(2\,\mathrm{m/s^2}\)
[Solution Description]
First, find the net force acting on the object: 6 N (right) - 2 N (left) = 4 N to the right. Using Newton's Second Law ($F = ma$), we can calculate the acceleration: $a = F/m = 4 N / 2 kg = 2 m/s^2$.

Key Concept: Force as Interaction Between 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 an object's speed, direction of motion, or shape only when interacting with another object. This is true because forces arise due to interactions, and their effects (as listed in the syllabus) occur during such interactions. The Reason correctly explains this by stating that forces result from the interaction between at least two objects, which aligns with the key concept mentioned in the syllabus.

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, 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: 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: Interaction forces, Newton's third law

a) Both forces disappear instantly
[Solution Description]
The book exerts a downward force on the table due to gravity (its weight), and the table exerts an equal and opposite normal force upward on the book (Newton's third law). If the table disappears, there is no interaction between the book and the table, so both forces cease to exist simultaneously.

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 existence conditions

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

Key Concept: Force Interaction between Objects

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

Key Concept: 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

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: 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: 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: Contact Forces

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

Key Concept: Muscular Force, 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: Electrostatic Force, Non-contact Forces

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

Key Concept: 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

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, 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: Muscular Force

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

Key Concept: Muscular Force

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

Key Concept: Friction, Motion Through Fluids, Conceptual Complexity

b) It doubles
[Solution Description]
Air resistance or drag force in most cases is directly proportional to velocity when the speed is low (viscous drag). If the speed of the object doubles, the air resistance also doubles. For higher speeds, drag may vary with the square of velocity, but the question specifies proportionality to velocity, so the correct interpretation is linear dependence.

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: 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: 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: 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: 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

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: 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: Magnetic force, Non-contact forces

b) 250 μN
[Solution Description]
We use the formula for magnetic force between two poles:
$F = \frac{\mu_0 \cdot m_1 \cdot m_2}{4\pi \cdot r^2}$
Here, $\mu_0 = 4\pi \times 10^{-7}$ N/A$^2$, $m_1 = m_2 = 5$ A·m, and $r = 0.1$ m. Plugging in these values:
$F = \frac{(4\pi \times 10^{-7}) \times 5 \times 5}{4\pi \times (0.1)^2}$
Simplify $4\pi$ terms:
$F = \frac{25 \times 10^{-7}}{(0.01)}$
Calculate numerator and denominator:
$F = 25 \times 10^{-5} \, \text{N} = 250 \times 10^{-6} \, \text{N} = 250 \, \mu\text{N}$
Therefore, the force is 250 μN.

Key Concept: Magnetic force, Pole interaction

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

Key Concept: Magnetic force definition

b) The force exerted by a magnet on another magnet or magnetic material
[Solution Description]
The magnetic force is defined as the force exerted by a magnet on another magnet or a magnetic material, even without direct contact. This makes it a non-contact force.

Key Concept: Magnetic force, Non-contact forces

a) The Earth's magnetic South pole is located at the geographic North pole
[Solution Description]
The Earth acts like a giant magnet with its magnetic South pole near the geographic North pole. A compass needle aligns itself along the Earth's magnetic field lines. The North-seeking pole of the compass needle is attracted to the Earth's magnetic South pole, which is why it points towards the geographic North pole.

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: Charging by Rubbing

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

Key Concept: 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: Electrostatic force, charge transfer

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

Key Concept: Weight Variation Across Planets

c) 19 N
[Solution Description]
First, find the mass of the object using the known weight on Earth:
$W = m \times g_{\text{Earth}} \\ \\ 50 = m \times 10 \\ \\ m = 5 \text{ kg}$
Now, calculate its weight on Mars using Mars' gravity:
$W_{\text{Mars}} = m \times g_{\text{Mars}} \\ \\ W_{\text{Mars}} = 5 \times 3.8 = 19 \text{ N}$
Thus, the object's weight on Mars is approximately 19 N.

Key Concept: Gravitational Force Definition

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

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

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

Key Concept: Gravitational Force

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: 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 vs mass, gravitational acceleration

c) Mass: 5 kg, Weight on Mars: 18.5 N
[Solution Description]
First calculate mass using Earth's gravity:
Weight = mass × acceleration due to gravity → mass = Weight/g = 49 N / 9.8 $m/s^2$ = 5 kg
Now calculate weight on Mars:
Weight on Mars = mass × Mars gravity = 5 kg × 3.7 $m/s^2$ = 18.5 N
Therefore, the mass is 5 kg and weight on Mars is 18.5 N.

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 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 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: Planetary Weight Variation

b) 3.8 N
[Solution Description]
On Venus, 1 kg mass corresponds to 9 N, so the mass of the object is $m = \frac{9\,N}{9\,N/kg} = 1\,kg$.
On Mars, 1 kg mass weighs 3.8 N. Hence, the weight of the object on Mars is $1\,kg \times 3.8\,N/kg = 3.8\,N$.

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: 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: 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: 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: 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: Measurement of weight, spring balance calibration

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

Key Concept: 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

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

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: 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:

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: 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, 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: 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: 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: Buoyant Force

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

Key Concept: 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

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: 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: $\frac{W}{F_b} = \frac{19.6}{69.8} = 0.28$.

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.