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 Motion

c) A force acted on the car to change its direction without changing its speed.
[Solution Description]
The question involves understanding the effect of force on an object's motion. Force can change the direction of motion without changing the speed. In this case, since the car's speed remains the same but its direction changes, a force must have acted perpendicular to the initial direction of motion. This force causes the change in direction but does not affect the magnitude of velocity.
Step-by-step reasoning:
1. Initially, the car moves at $10 \, \text{m/s}$ in one direction.
2. After the change, it moves at $10 \, \text{m/s}$ in a perpendicular direction.
3. Since the direction changed, a force must have acted on the car to cause this change, even though the speed remained the same.

Key Concept: 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: 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: Types of Force

c) Opening a drawer
[Solution Description]
Pulling refers to exerting force towards oneself. Among the options, opening a drawer requires pulling it outward, whereas pressing a balloon or kicking a ball involves push forces. Stretching a rubber band also involves pulling.

Key Concept: Types of Force: Push and Pull

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
According to the syllabus, a **pull** is defined as a force that brings an object closer to the source of the force. Lifting an object involves applying an upward force (pull) to bring it closer to the person or device exerting the force. Therefore, lifting qualifies as a pull. The reason correctly explains the assertion since the action of lifting aligns with the definition of a pull.

Key Concept: 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: 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: Examples of Force

c) Pedaling a bicycle to move forward
[Solution Description]
From the syllabus, examples of force include moving a box by pushing or pulling and pedaling a bicycle. These actions involve applying a push or pull.
Thus, the correct answer should describe an action involving push or pull.

Key Concept: Force interaction, Effects of force

b) Speed decreases, direction remains same initially
[Solution Description]
The wind applies a contact force opposite to the bicycle's motion. According to force concepts: 1) The bicycle was moving at constant speed (balanced forces). 2) Wind introduces unbalanced force opposite to motion. 3) This will cause deceleration (speed decreases) while maintaining same direction initially. If wind continues, it may eventually stop or reverse direction.

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 and its Effects

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

Key Concept: Effects of Force

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: 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: 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

c) It changes both the speed and direction of the ball
[Solution Description]
Kicking a moving football applies a force that can change both the speed and direction of the ball depending on how the kick is delivered. However, the primary effect described here is changing the direction of the ball's motion.

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

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 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: Change in motion, Direction of force

c) The ball moves northwest with a force of approximately 58 N
[Solution Description]
To find the net effect on the ball's motion:
Step 1: The ball is initially stationary. The northward force (50 N) will make it move north.
Step 2: The westward force (30 N) acts perpendicularly to the northward force.
Step 3: The resultant direction will be northwest since both forces combine vectorially.
Step 4: The magnitude of the resultant force can be calculated using the Pythagorean theorem: $\sqrt{50^2 + 30^2} = \sqrt{2500 + 900} = \sqrt{3400} \approx 58.31$ N.
Therefore, the ball will move in the northwest direction with a force of approximately 58.31 N.

Key Concept: 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: 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: 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 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: Action-Reaction Pairs, Non-contact Forces

a) Both magnets experience 1 N force in opposite directions
[Solution Description]
Magnetic force is an interaction between two objects following Newton's third law. Even if one magnet is stronger, the force exerted by Magnet A on Magnet B equals the force exerted by Magnet B on Magnet A. Therefore, both magnets will experience 1 N force in opposite directions, not 1.5 N or any unequal values. The action-reaction pair remains equal in magnitude.

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: 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

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: 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: Force Interaction

c) Balanced forces are acting on the book.
[Solution Description]
The book is at rest, which means the forces acting on it are balanced. The gravitational force pulling the book downward is equal in magnitude but opposite in direction to the normal force exerted by the table pushing the book upward.

Key Concept: Force interaction, SI unit

d) newton (N)
[Solution Description]
Since both forces (A on B and B on A) are part of the same interaction pair, they must have the same SI unit. The SI unit of force is newton (N).

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: SI Unit of Force

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

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: 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 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: 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: Gravitational Force

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

Key Concept: Gravitational Force, 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: 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: 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: 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

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 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

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that muscular force is a contact force, which is true as it requires physical interaction between objects like when we push or pull something using our muscles. The reason explains that muscular force arises from muscle contractions and elongations, which is also correct. Moreover, the reason correctly justifies why muscular force qualifies as a contact force since muscle action involves direct interaction with other objects. Therefore, both the assertion and reason are true, and the reason is the correct explanation of the assertion.

Key Concept: Muscular force, 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

b) The force caused by the action of muscles in our body
[Solution Description]
Muscular force is the force exerted by the contraction and elongation of muscles during physical activities like walking, lifting, or pushing. It is a type of contact force since it occurs when muscles interact with objects or body parts.

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 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: Friction and Surface Texture

a) Glass surface because it has lower friction.
[Solution Description]
Friction depends on the roughness of the surfaces in contact. Glass is smoother than sandpaper, so the frictional force acting on the block is less on the glass surface compared to the sandpaper surface. With lower friction, the block can travel farther before stopping.

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: 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 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

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: Non-contact Forces: Magnetic Force

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that a magnet can exert force on another magnet without contact, which is true as demonstrated in Activity 5.5. The reason states that magnetic force is a non-contact force, which is also true according to the syllabus. Moreover, the reason correctly explains why the assertion is valid since the non-contact nature of magnetic force allows it to act without physical contact. Thus, both are true, and the reason explains the assertion.

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

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

Key Concept: Non-contact 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 - Pole interaction

c) The second magnet will be pulled downward
[Solution Description]
When unlike poles (North-South) of magnets face each other, they attract. Thus, the second magnet will not remain floating but will be pulled towards the first magnet.

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

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 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: Types of Charges

b) Positive and Negative
[Solution Description]
The two kinds of static charges are positive and negative. This classification explains why like charges repel and unlike charges attract.

Key Concept: Electrostatic force, Charging by friction, Interaction of charges

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
During the experiment, when two balloons are rubbed with a woollen cloth, both balloons acquire static charges. Since they are charged using the same material (woollen cloth), they develop the same type of charge (like charges). According to the principle of electrostatics, like charges repel each other. Therefore, both Assertion and Reason are true, and Reason correctly explains why the balloons repel each other.

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: 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: Gravitational Force and Weight

c) 8 N
[Solution Description]

Key Concept: Gravitational force, Weight measurement

b) 10 N
[Solution Description]
From the given table, we know that an object with mass $1 kg$ weighs $10 N$ on Earth and $25.4 N$ on Jupiter. Since the question states the object's mass is $1 kg$, its weight on Earth would be $10 N$. The weight changes due to different gravitational forces, but mass remains constant.

Key Concept: Weight vs mass, gravitational acceleration

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

Key Concept: Spring Balance

b) 700 g
[Solution Description]
To find the mass of the object:
1. Given that the weight of the object is $7 N$.
2. Use the formula $\text{Mass} = \frac{\text{Weight}}{\text{Gravity}} = \frac{7 N}{10 N/kg} = 0.7 kg = 700 g$.

Key Concept: 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 Measurement, Gravitational Force

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
Step 1: Understand the concept of weight. Weight ($W$) is given by the formula $W = m \times g$, where $m$ is mass and $g$ is acceleration due to gravity.
Step 2: Analyze the Assertion. Since $g$ on the Moon ($1.6$ m/s²) is less than $g$ on Earth ($10$ m/s²), for a given mass $m$, the weight $W$ will indeed be less on the Moon than on Earth. Thus, the Assertion is true.
Step 3: Examine the Reason. The Reason states the correct values of $g$ for the Moon and Earth, which are accurate. It also correctly explains why the weight differs between the two celestial bodies. Hence, the Reason is true and provides a valid explanation for the Assertion.

Key Concept: Weight and Its Measurement

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that weight is measured in newtons (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: Spring balance measurement, weight vs mass

c) 2.56 N
[Solution Description]
From the table: On Earth, $1 kg$ weighs $10 N$, so 16 N corresponds to $1.6 kg$ mass ($\frac{16}{10}$). On Moon, $1 kg$ weighs $1.6 N$, so $1.6 kg$ would weigh:
$1.6 kg \times 1.6 N/kg = 2.56 N$

Key Concept: Comparative weights, unit conversion

c) 2.54 times
[Solution Description]
On Earth: Weight = $5 kg \times 10 N/kg = 50 N$
On Jupiter: Weight = $5 kg \times 25.4 N/kg = 127 N$
Increase factor:
$\frac{127 N}{50 N} = 2.54$

Key Concept: 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: Mass Consistency, Weight Calculation

a) 5 kg, 8 N
[Solution Description]
Mass is constant regardless of location, so the mass remains 5 kg. Weight changes based on gravity. The weight on the Moon is calculated using $Weight = Mass \times Gravitational \ Acceleration$. For the Moon, $Weight = 5 \ kg \times 1.6 \ N/kg = 8 \ N$. Thus, the mass is 5 kg and the weight is 8 N.

Key Concept: Assertion-Reason

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that the weight of an object changes on different planets. This is true because weight depends on the gravitational force acting on the object, which varies from planet to planet (e.g., Earth's gravity is stronger than the Moon's).
The reason states that the mass remains constant while gravitational force changes. This is also correct because mass is independent of location, whereas weight ($W = m \times g$) depends on both mass ($m$) and gravitational acceleration ($g$), which differs for each planet. Moreover, the reason correctly explains why the assertion is true—since $g$ changes, weight changes even if mass stays the same.
Therefore, both the assertion and reason are true, and the reason is the correct explanation of the assertion.

Key Concept: 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: Difference between weight and mass

d) Assertion is false, but Reason is true.
[Solution Description]
The assertion states that the weight of an object is the same on Earth and the Moon. This is false because weight varies with gravitational force, which is different on Earth and the Moon. The reason states that mass is the amount of matter in an object, while weight depends on gravity, which is true and correctly explains why the assertion is false. Therefore, the correct option is d).

Key Concept: Measurement of weight, spring balance calibration

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

Key Concept: 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: Mass vs. Weight, Spring Balance Measurement

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that the weight of a 1 kg object on Mars is approximately 3.8 N, which is correct as per the given data from the syllabus table (Mars: 1 kg object weighs 3.8 N).
The reason explains that a spring balance measures gravitational force (weight), and the gravitational acceleration on Mars is about 3.8 m/s$^2$. This is also correct because the weight ($W$) of an object is calculated as $W = mg$, where $m$ is mass (constant everywhere) and $g$ is the gravitational acceleration. For Mars, $g \approx 3.8 m/s^2$, so $W = 1 \times 3.8 = 3.8 N$.
The reason correctly explains why the assertion is true since it provides the underlying physics principle linking mass to weight via gravitational acceleration.

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: Buoyant Force, Archimedes' Principle

c) 20 N
[Solution Description]
First, calculate the buoyant force in water when fully submerged:
Buoyant force = Weight in air - Apparent weight in water = $50 N - 30 N = 20 N$
Since buoyant force equals weight of displaced fluid, for half-submerged case in denser liquid:
New buoyant force = (Original buoyant force / 2) * (Density ratio) = $(20 N / 2) * 2 = 20 N$

Key Concept:

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

Key Concept:

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 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: 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: 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: 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: 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: 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: 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 $\tau_W - \tau_b = 2500AL^2 \sinθ - 5000A \frac{H^2}{\cos^2θ} \sinθ$.