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: Force Definition

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 applied on an object. This is correct according to the key points in the syllabus. The reason states that forces can change the speed, direction, or shape of an object, which is also correct as per the syllabus. Further, the reason correctly explains why a force is defined as a push or pull because these actions (push/pull) lead to changes in speed, direction, or shape. Thus, both the assertion and reason are true, and the reason correctly explains the assertion.

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: Force, Change in Shape

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

Key Concept: Force - Push and Pull

d) Assertion is false, but Reason is true.
[Solution Description]
The Assertion states that a force always changes the speed of an object, which is not necessarily true. A force can also change the direction or shape of an object without changing its speed. The Reason correctly defines force as a push or pull applied on an object, which is accurate. However, the Reason does not explain why the Assertion would be true because the Assertion itself is false.

Key Concept: Push and Pull Forces, Force Interactions

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that pushing requires more force than pulling for moving a heavy box. This is because when you push, part of your force adds to the weight of the box, increasing the normal force and thus increasing friction. On the other hand, when you pull, the vertical component of the force lifts the box slightly, reducing the normal force and hence decreasing friction. Therefore, both Assertion and Reason are true, and the Reason correctly explains the Assertion.

Key Concept: Force interaction, Muscular force, Type of force

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

Key Concept: 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: 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: 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: Muscular force, Contact forces

c) Contact forces act both during lifting and holding
[Solution Description]
When lifting: 1) Muscular force overcomes gravity (contact force through hands). 2) Forces are unbalanced during lifting. 3) When stationary: muscular force equals gravitational pull (balanced forces). 4) Only contact forces act throughout - muscles (biological) and normal force. The barbell doesn't move because forces balance.

Key Concept: 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: 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: 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: 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: Changing shape and combination of effects

d) Only changes the shape of the rubber band
[Solution Description]
When a force is applied to stretch a rubber band, it changes the shape of the rubber band (deformation). Additionally, if the rubber band was initially at rest, the force also causes it to move (change in speed). However, the primary observable effect is the change in shape.

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: 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: 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, 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: Force and its Effects

d) Assertion is false, but Reason is true.
[Solution Description]
The Assertion states that applying a force on a moving object always increases its speed. However, this is not always true because a force can also decrease the speed (e.g., brakes on a bicycle), change the direction (e.g., hitting a ball with a bat), or change the shape (e.g., pressing a balloon). The Reason correctly explains the various effects a force can have on an object, but it does not support the Assertion, which is false as it generalizes only one possible effect of force.

Key Concept: Effect of Force

c) Make the object move from rest.
[Solution Description]
A force applied to a stationary object can make it move from rest. For example, pushing a chair moves it from its initial position.

Key Concept: Force Changing Direction

c) The ball’s direction changes
[Solution Description]
When a moving tennis ball is hit by a racket, the force applied by the racket primarily changes the direction of the ball's motion. According to the syllabus, force can alter the direction of a moving object, as seen in the example of hitting a moving ball with a bat.

Key Concept: Types of Forces

c) Gravitational force
[Solution Description]
Non-contact forces act without direct physical contact. Examples include gravitational force, magnetic force, and electrostatic force, whereas muscular and frictional forces require contact.

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 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: 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: 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: 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: Interaction forces, Action-reaction pairs

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

Key Concept: Balanced forces, Net force

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

Key Concept: 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 as Interaction

c) A push or pull resulting from the interaction between two or more objects
[Solution Description]
A force is a push or pull resulting from the interaction between two or more objects.

Key Concept: Force Interaction

c) The wall pushes back with equal force
[Solution Description]
According to Newton's third law, every action has an equal and opposite reaction. When the man pushes the wall, the wall exerts an equal and opposite force on the man. Since the wall doesn't move, the reaction force is equal in magnitude to the force applied by the man but in the opposite direction.

Key Concept: SI Unit of Force

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

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 Units and Nature

b) The unit is newton (N) and forces can act with or without contact.
[Solution Description]
The SI unit of force is the newton (N), which measures the interaction between two objects resulting in a push or pull. Forces can act through contact (like pushing a table) or at a distance (like gravity).

Key Concept: Forces as 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: Example of Force

c) A magnet attracting an iron nail
[Solution Description]
A force results from the interaction between at least two objects. Among the given options, a magnet attracting an iron nail involves two objects (magnet and nail) interacting, resulting in a force. The other options either involve single objects or no interaction.

Key Concept: Types of Forces

c) Gravitational force
[Solution Description]
Non-contact forces are those that act on objects without physical contact. Examples include gravitational force, magnetic force, and electrostatic force.

Key Concept: Magnetic force, Electrostatic force

d) Both non-contact forces act simultaneously
[Solution Description]
The iron ball experiences magnetic attraction regardless of charge due to its ferromagnetic property. If charged, it also experiences electrostatic force - repulsion if like-charged with the magnet, attraction if oppositely charged. The net force depends on relative strengths, but both non-contact forces are always present.

Key Concept: Gravitational Force

b) Newton
[Solution Description]
Weight is the gravitational force with which the Earth attracts an object. The SI unit of weight (and force in general) is the newton, represented by the symbol $N$.

Key Concept: Frictional force, Muscular force, Gravitational force

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

Key Concept: 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: 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: 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

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: 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

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, 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: Factors Affecting Friction

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

Key Concept: Friction, Multi-Surface Comparison, Numerical Difficulty

c) $2.4\, \text{m/s}^2$
[Solution Description]
The forces acting on the box are gravity ($mg \sin\theta$) down the incline and kinetic friction ($f_k = \mu_k N$) opposing motion. Normal force $N = mg \cos\theta$. Net force along the incline is $F_{\text{net}} = mg \sin\theta - \mu_k mg \cos\theta$. Acceleration $a = \frac{F_{\text{net}}}{m} = g (\sin\theta - \mu_k \cos\theta)$. Substituting $\theta = 30^\circ$, $\sin30^\circ = 0.5$, $\cos30^\circ \approx 0.866$, and $\mu_k = 0.3$, we get:
$a = 10 (0.5 - 0.3 \times 0.866) = 10 (0.5 - 0.2598) = 10 \times 0.2402 \approx 2.402\, \text{m/s}^2.$

Key Concept: 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: 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, 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: 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: Gravitational Force

c) Gravitational force
[Solution Description]
Gravitational force is the non-contact force exerted by the Earth that attracts objects towards its center. This is why a ball thrown upwards eventually falls back to the ground.

Key Concept: 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: Magnetic Force

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

Key Concept: Magnetic force, Pole interaction

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

Key Concept: 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 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: 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: 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 and Repulsion

c) Assertion is true, but Reason is false.
[Solution Description]
The Assertion states that a charged balloon repels another similarly charged balloon, which is true as per the observation in Activity 5.7 where two rubbed balloons repel each other. The Reason claims that like charges attract each other, but according to the inference from the activity, like charges repel each other, not attract. Hence, the Assertion is true, but the Reason is false.

Key Concept: Gravitational Force and Weight

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 is the force with which the Earth attracts it, which is true as weight is defined as the gravitational force exerted by the Earth on an object. The reason given is that weight is measured in newtons ($N$) because it is a force, which is also true. Furthermore, the reason correctly explains why weight is measured in newtons since the unit newton is used for measuring force. Therefore, both the assertion and reason are true, and the reason is the correct explanation of the assertion.

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 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: Non-contact force, Gravitational behavior

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

Key Concept: Weight 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: 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: Gravitational Force Comparison

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

Key Concept: Weight vs. Mass

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

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 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: 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: Spring Balance Measurement

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

Key Concept: 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: Planetary Weight Comparison

a) 6.68
[Solution Description]
The weight on a planet is given by $Weight = Mass \times Gravitational \ Acceleration$. Since mass is constant, the ratio of weights is equal to the ratio of gravitational accelerations. Given weights are 25.4 N (Jupiter) and 3.8 N (Mars). The ratio is $\frac{25.4 \ N}{3.8 \ N} = 6.684$, approximately 6.68 when rounded to two decimal places.

Key Concept: Weight calculation on different planets

a) 76.2 N
[Solution Description]
The weight on Jupiter is calculated by multiplying the gravitational ratio (2.54) by the weight on Earth. Therefore, $30 \, \text{N} \times 2.54 = 76.2 \, \text{N}$.

Key Concept: 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, 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: Spring balance operation, weight measurement

c) 4.76 N
[Solution Description]
Difference between 4.6 N and 4.8 N = 0.2 N. With 5 divisions, each represents $\frac{0.2 N}{5} = 0.04 N$. The pointer is closest to 4.8 N minus one division (since it's below 4.8 N), so reading = $4.8 N - 0.04 N = 4.76 N$.

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: Buoyant Force

c) The balance between gravitational force and buoyant force
[Solution Description]
Whether an object floats or sinks depends on the balance between its gravitational force (weight) and the buoyant force exerted by the liquid. If the buoyant force is greater than or equal to the object's weight, it floats; otherwise, it sinks.

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: Density Comparison, Floating Condition

b) $\rho_A > \rho_w > \rho_C > \rho_B$
[Solution Description]
According to floating conditions:
1. For sinking object: $\rho_A > \rho_w$
2. For partially floating object: $\rho_B = \frac{1}{2}\rho_w$ (since half volume displaces equal weight)
3. For fully floating object: $\rho_C \rho_w > \rho_C > \rho_B$

Key Concept:

c) The 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: 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: 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: Density and Buoyancy

a) Higher density increases buoyant force
[Solution Description]
The buoyant force depends on the density of the liquid. A denser liquid exerts a greater buoyant force because it can displace more mass for the same volume compared to a less dense liquid.

Key Concept: 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:
$\text{Density of A} > \text{Density of water} > \text{Density of B}.$

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

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.