Key Concept: Force, Multiple Effects

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

Key Concept: Force 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: 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: 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 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, 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: 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: 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: Effects of Force

d) Changing the color of the object.
[Solution Description]
Applying force on an object can cause it to move from rest, change its speed or direction, or alter its shape. However, changing the color of an object is not an effect of force; it usually involves chemical or optical processes. Therefore, this option is correct as it does not align with the known effects of force.

Key Concept: SI Unit of Force

c) Newton
[Solution Description]
The syllabus states that the SI unit of force is newton, represented by the symbol $N$.
Hence, the correct option must specify "newton" as the unit.

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: Change in Direction of Motion

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

Key Concept: Effect of Force 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: Effect of Force

b) The object may start moving
[Solution Description]
Applying a force on an object at rest can make it move. From the syllabus, we know that force can cause an object to move from rest.

Key Concept: Effects of Force

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

Key Concept: 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: Change in Shape Due to Force

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

Key Concept: Effect of Force

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 forces can either increase or decrease the speed of an object. The reason gives an example of applying brakes, which is a force acting to slow down the bicycle, thus changing its speed. Therefore, both the assertion and reason are true, and the reason correctly explains the assertion.

Key Concept: Effect of Force

b) It brings the ball to rest
[Solution Description]
When a fielder stops a moving cricket ball by catching it, the force applied opposes the motion of the ball, causing it to slow down and eventually stop. This means the force decreases the speed of the ball.

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 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: 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: Assertion-Reason

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.
[Solution Description]
The assertion states that a force can change the direction of motion of a moving object, which is true as seen in examples like hitting a ball with a bat. The reason states that when a fielder stops a moving ball, the force applied changes its speed, which is also true. However, the reason does not correctly explain the assertion because the assertion is about changing direction while the reason is about changing speed. Therefore, both are true but the reason does not explain the assertion.

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, 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 and Unbalanced Forces

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

Key Concept: Balanced forces, 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: 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: Balanced vs. Unbalanced Forces

c) The forces acting on the car are balanced.
[Solution Description]
When an object moves with constant speed in a straight line, it means the net force acting on it is zero. The driving force from the engine is balanced by opposing forces such as friction and air resistance.

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: 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: SI Unit of Force

c) Newton
[Solution Description]
The SI unit of force is newton, represented by the symbol $N$.

Key Concept: 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 SI unit of force is newton ($N$), which is correct as per the syllabus. The reason states that force is an interaction involving a push or pull between two objects, which is also true. Moreover, the reason correctly explains why the unit is named newton since it quantifies such interactions.

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 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: 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: Force pairs, Action-reaction

c) Reaction force from water pushes you forward
[Solution Description]
When you push the water backward (action force), according to Newton's third law, the water exerts an equal and opposite reaction force on you, pushing you forward. This forward force propels you through the water. The movement occurs because the forces are interaction pairs acting on different objects (you and the water).

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: 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: 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: 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 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: Contact Forces

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

Key Concept: Assertion-Reason

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The Assertion states that frictional force always opposes the relative motion between two surfaces in contact, which is true because friction acts in the direction opposite to the motion or attempted motion of an object. The Reason explains that frictional force arises due to microscopic irregularities and interlocking between surfaces, which is also true and correctly explains why friction opposes motion. Therefore, both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

Key Concept: 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, External applications

c) Muscular force, as the oxen contract their muscles to move
[Solution Description]
Oxen use their muscles to generate the force required to pull the plow. Since muscular force is defined as the force resulting from muscle action, the oxen's effort to move the plow is a direct application of muscular force.

Key Concept: Muscular Force

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

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: Surface Nature and Friction

c) Increases friction
[Solution Description]
Friction depends on the nature of the surfaces in contact. Rough surfaces have greater friction compared to smooth surfaces due to more interlocking of irregularities.

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: 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: Friction and Surface Interaction

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The Assertion states that friction reduces the speed of a moving object on a rough surface, which is true because friction opposes motion. The Reason explains why rough surfaces cause more friction by pointing out the increased irregularities leading to greater interlocking, which is also true. Additionally, the Reason correctly explains why the Assertion occurs, as it links the effect (reduced speed) with its cause (greater friction due to surface roughness). Therefore, both the Assertion and Reason are true, and the Reason is the correct explanation of the 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, Gravitational force

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.
[Solution Description]
The Assertion states that a magnet can attract an iron nail without touching it, which is true because magnetic force acts at a distance (non-contact). The Reason states that gravitational force is a non-contact force, which is also true as the Earth pulls objects without direct contact. However, the Reason does not explain why the Assertion is correct since gravitational force and magnetic force are two different phenomena. Thus, both statements are true, but the Reason does not correctly explain the Assertion.

Key Concept: 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: Electrostatic Force

b) They repel each other
[Solution Description]
When two balloons are rubbed with a woollen cloth, they acquire like charges. According to the principle of electrostatics, like charges repel each other, so the balloons will repel each other when brought close.

Key Concept: 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: Non-contact force

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

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

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The Assertion states that the second ring magnet floats above the first magnet when their like poles face each other due to repulsive magnetic force. This is true because like poles repel each other, creating a force that opposes gravity. The Reason explains that like poles repel each other, which is correct, and further states that this repulsion balances the gravitational force, which is also accurate. Therefore, both the Assertion and Reason are true, and the Reason correctly explains the Assertion.

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: Electrostatic Force: Attraction

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

Key Concept: Electrostatic Force Basics

c) Electrostatic force
[Solution Description]
The electrostatic force is the force exerted by a charged body on another charged or uncharged body. It is a non-contact 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: 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, 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 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: 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: 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 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: 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 Measurement

b) $0.1 N$
[Solution Description]
The smallest measurable weight is calculated by dividing the range by the number of divisions: $\frac{1 N - 0 N}{10} = 0.1 N$.

Key Concept: 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 Measurement and Gravitational Force

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that the weight of an object on the Moon is less than its weight on Earth, which is true because weight depends on the gravitational force acting on the object. The reason explains that the gravitational force on the Moon is weaker than on Earth, which is also true and correctly justifies the assertion. This is evident from the given table where 1 kg mass weighs 1.6 N on the Moon compared to 10 N on Earth. Therefore, both the assertion and reason are true, and the reason is the correct explanation of the assertion.

Key Concept: Weight 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: Difference between Mass and Weight

c) Mass remains constant, but weight changes depending on gravity.
[Solution Description]
Mass is the amount of matter in an object and remains constant, while weight depends on gravitational force and can vary.

Key Concept: Weight 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: Difference between weight and mass

b) 8.33 N
[Solution Description]
Weight is calculated using the formula $W = m \times g$. On Earth, the weight would be $5 \, \text{kg} \times 10 \, \text{m/s}^2 = 50 \, \text{N}$. On the Moon, the gravitational acceleration is $\frac{1}{6} \times 10 = \frac{10}{6} \, \text{m/s}^2 \approx 1.67 \, \text{m/s}^2$. Thus, the weight on the Moon is $5 \, \text{kg} \times 1.67 \, \text{m/s}^2 \approx 8.35 \, \text{N}$.

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: 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: Weight vs mass, planetary differences

b) 10 kg
[Solution Description]
Weight = mass × gravity. To find mass, rearrange: $m = \frac{W}{g} = \frac{38 N}{3.8 m/s^2} = 10 kg$.

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: Spring Balance Smallest Division

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

Key Concept: 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:

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:

c) The buoyant force is greater than the gravitational force.
[Solution Description]
The bottle experiences two main forces: gravitational force (weight) downward and buoyant force (upthrust) upward. When released, the bottle bounces back to the surface because the buoyant force is greater than its weight. According to Archimedes’ principle, the buoyant force equals the weight of the displaced water. Hence, if the object floats, the buoyant force must balance or exceed the gravitational force.

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: 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, Archimedes' Principle

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

Key Concept: 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: 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: Multi-concept: Archimedes' Principle, Pressure

c) $2500A(L^2 - 2\frac{H^2}{\cos^2θ})\sinθ$
[Solution Description]
Three forces act: Weight ($W = \rho_r ALg$) downward at $\frac{L}{2}$, Buoyant force $F_b=\rho_w A\left(\frac{H}{\cos\theta}\right)g$ upward at $\frac{H}{2\cos\theta}$, and hinge reaction. Torque due to weight: $\tau_W = W \times \frac{L}{2} \sinθ = 500AL \times 10 \times \frac{L}{2} \sinθ = 2500AL^2 \sinθ$. Torque due to buoyancy: $\tau_b = F_b \times \frac{H}{2\cosθ} \sinθ = 1000A\frac{H}{\cosθ} \times 10 \times \frac{H}{2\cosθ} \sinθ = 5000A \frac{H^2}{\cos^2θ} \sinθ$. Net torque is $\tau_W - \tau_b = 2500AL^2 \sinθ - 5000A \frac{H^2}{\cos^2θ} \sinθ$.

Key Concept: Archimedes' Principle, Density

d) 1.00
[Solution Description]
Let h be the height submerged in water. The volume submerged is $V_s = (0.1)^2 \times h$. The weight of displaced water plus oil equals the block's weight: $\rho_w V_s g + \rho_o ((0.1)^3 - V_s)g = \rho_b (0.1)^3 g$. Substituting values: $(1000)(0.01h)g + (800)(0.001 - 0.01h)g = (600)(0.001)g$. Simplifying: $10h + 0.8 - 8h = 0.6$ → $2h = -0.2$ → $h = 0.1$ m = 10 cm. Thus, the entire block is submerged in water.

Key Concept: 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 Comparison

c) Density of A is greater than density of B
[Solution Description]
For an object to float, its average density must be less than or equal to the density of water ($1000 \text{ kg/m}^3$). If an object sinks, its density is greater than that of water. Therefore:
$\text{Density of A} > \text{Density of water} > \text{Density of B}.$