Key Concept: Force Definition

b) A push or pull applied on an object
[Solution Description]
A force is defined as a push or pull applied on an object, resulting from its interaction with another object. It can change the speed, direction of motion, or shape of the object.
The correct answer corresponds to the definition provided in the syllabus: "Generally, the push or pull applied on an object is called force in science."

Key Concept: 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: 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: Unit of Force

c) Newton (N)
[Solution Description]
The SI unit of force is newton, symbolized as $N$. It is named after Sir Isaac Newton, who formulated the laws of motion.

Key Concept: Effect of Force

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

Key Concept: Force - 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: 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: 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: 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 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: 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, 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: 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: 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: 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 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: 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 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: Change in Shape Due to Force

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

Key Concept: 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 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: 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: 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: 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: SI Unit of Force

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

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

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

Key Concept: Balanced forces, Net force

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

Key Concept: 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: Definition of Force

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

Key Concept: Balanced and Unbalanced Forces

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

Key Concept: Force Interaction, SI Unit of Force

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

Key Concept: 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 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: Buoyant Force

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

Key Concept: Force Interaction 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: 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: 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: 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: Gravitational Force, Electrostatic Force

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
Gravitational force acts between any two masses and is always attractive, as stated in the syllabus. Electrostatic force, however, depends on the charges involved: like charges repel, and unlike charges attract, making it either attractive or repulsive. The reason correctly states that gravitational force depends on mass and electrostatic force depends on charge. Thus, both Assertion and Reason are true, and Reason explains why the Assertion is correct.

Key Concept: Contact Forces and Muscular Force

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
Muscular force is indeed a contact force because it requires direct or indirect physical interaction between objects (such as hands lifting a box). The Reason correctly explains why the Assertion is true—muscular force arises due to muscle contraction or elongation during physical activity, which necessitates contact. Therefore, both statements are true, and the Reason is the correct explanation of the Assertion.

Key Concept: Muscular Force

c) Muscular force
[Solution Description]
Muscular force is a contact force generated by the action of muscles when they contract or elongate during activities like lifting, pushing, or pulling.

Key Concept: Contact and Non-Contact Forces

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

Key Concept: Contact Forces

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: 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

c) Friction increases as the surface gets rougher
[Solution Description]
Friction increases with roughness because irregularities between surfaces cause more resistance to motion.

Key Concept: Muscular Force

a) Lifting a bucket of water
[Solution Description]
Muscular force is exerted by muscles when performing physical activities like lifting, pushing, or pulling. Among the given options, lifting a bucket involves the contraction and elongation of muscles to apply force.

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 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, 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: 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: 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: Friction, Air Resistance

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

Key Concept: Basic Concept: Direction of Friction

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

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

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

Key Concept: Magnetic force, 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 - 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, 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: Non-contact force

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

Key Concept: 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 Rubbing

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

Key Concept: Electrostatic force, 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: 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, Spring balance principle

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

Key Concept: Vertical Motion Under Gravity

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

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

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

Key Concept: Gravitational Force Calculation

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

Key Concept: Weight Definition

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

Key Concept: Weight 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: 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: Weight vs Mass, Gravitational Variation

a) 266 N
[Solution Description]
First, understand that mass remains the same everywhere, but weight changes due to gravity. The astronaut's mass is given as 70 kg. On Mars, the gravitational force per unit mass is 3.8 N/kg. To find the weight, multiply the mass by the gravitational acceleration on Mars: $Weight = Mass \times Gravitational \ Acceleration$. So, $Weight = 70 \ kg \times 3.8 \ N/kg = 266 \ N$.

Key Concept: Definition of Weight

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

Key Concept: Measurement of weight 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: 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: Floating and Sinking

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

Key Concept: Archimedes’ Principle

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

Key Concept:

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 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: 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: 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, Relative density

c) 1.0
[Solution Description]
The loss in weight (buoyant force) is $120 - 80 = 40$ N.
From Archimedes' Principle, $F_b = \rho_l \cdot V \cdot g$.
The volume of the object ($V$) can be found from its weight: $m = \frac{120}{g}$.
The relative density of the object is 3, so its density is $3 \times 1000 = 3000$ kg/m$^3$.
Volume $V = \frac{m}{\rho_s} = \frac{120/g}{3000} = \frac{120}{3000g}$.
Now, substitute into buoyant force equation: $40 = \rho_l \cdot \frac{120}{3000g} \cdot g$.
Simplifying, $\rho_l = \frac{40 \times 3000}{120} = 1000$ kg/m$^3$.
Relative density of liquid is $\frac{\rho_l}{\rho_{water}} = 1$.

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, Buoyant Force

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that a steel ship floats because its average density is less than water. This is true because ships are designed with hollow structures, reducing their average density below that of water. The reason states that the buoyant force equals the weight of displaced water, which is the correct explanation for why the ship floats (Archimedes' Principle). Thus, both statements are true, and the reason correctly explains the assertion.

Key Concept: Archimedes' Principle

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The Assertion states that a 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 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.