Class 8 Science Chapter 5 Exploring Forces (New Course)

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

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

Key Concept: Force, Friction, Interaction of Forces

d) Assertion is false, but Reason is true.
[Solution Description]
The Assertion states that a rolling ball stops due to gravitational force. This is incorrect because the stopping is caused by frictional force, not gravitational force. Gravitational force acts vertically downward and does not oppose horizontal motion. The Reason claims that gravitational force opposes the motion of objects in contact with the ground, which is also false since friction opposes motion, not gravity. Thus, both Assertion and Reason are false.

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: 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: 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

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: 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: Muscular Force

c) Lifting a box from the ground.
[Solution Description]
Muscular force is the force exerted by muscles in the body during physical activities. Among the given options, lifting a box requires contraction and elongation of muscles, making it an example of muscular force. The other options involve forces like gravitational force (apple falling) and contact force (pressing keys), but not necessarily muscular force.

Key Concept: Force and Its Effects

c) The wind decreases her speed unless she pedals harder.
[Solution Description]
The wind applies a force opposite to Ragini’s direction of motion. According to the concept of force, applying a force can change the speed or direction of a moving object. Here, the wind acts as an opposing force, which means Ragini must pedal harder to maintain or increase her speed. Thus, the wind decreases her speed unless she applies additional muscular 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: Definition of Force

c) A push or pull applied on an object
[Solution Description]
According to the syllabus, a force is defined as a push or pull applied on an object resulting from the object’s interaction with another object. The SI unit of force is newton ($N$).
Therefore, the correct choice is the option that mentions “push or pull” as the scientific definition of force.

Key Concept: Change in Shape

c) The shape of the object changes
[Solution Description]
Applying force can change the shape of an object. The syllabus states that force can bring about a change in the shape of an object, such as pressing an inflated balloon.

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: 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: 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

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 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: Changing direction and speed

c) Changes both the speed and direction of the car
[Solution Description]
The car’s initial velocity ($v_i$) = 20 m/s north. Final velocity ($v_f$) = 10 m/s west. The change involves both a reduction in speed and a change in direction (from north to west). Therefore, the net effect of the force is a combination of changing speed and direction.

Key Concept: 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: 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: Balanced forces, Stopping motion

c) The braking force opposes the motion, leading to deceleration
[Solution Description]
Step 1: The cyclist is initially moving at a constant speed, meaning the forces acting on the bicycle are balanced (no acceleration).
Step 2: When brakes are applied, friction acts opposite to the direction of motion.
Step 3: This unbalanced force reduces the speed until the bicycle stops.
Hence, the braking force opposes the motion, causing deceleration and ultimately stopping the bicycle.

Key Concept: 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: Change in Shape Due to Force

b) Stretching a rubber band
[Solution Description]
From the given syllabus examples, pressing an inflated balloon causes a change in its shape. This occurs because the applied force deforms the elastic material of the balloon temporarily. Thus, this situation clearly illustrates how force can alter the shape of an object.

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: 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: Force as Interaction

b) At least two objects must interact.
[Solution Description]
A force arises due to interaction between two objects. Without interaction, there is no force. The concept states that at least two objects must interact for a force to exist.

Key Concept: 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: 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: 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 and Unbalanced Forces

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that an object moving with constant velocity must be experiencing balanced forces. This is true because when forces are balanced, there is no net force acting on the object, resulting in no acceleration (constant velocity or at rest). The reason states that balanced forces result in no change in the state of motion of an object, which is also true and correctly explains why the assertion is true. Therefore, both the assertion and reason are true, and the reason is the correct explanation of the assertion.

Key Concept: 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: 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: 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: Force interaction, Newton’s third law

d) The book exerts a force of 5 N downward on the table
[Solution Description]
According to Newton’s third law, for every action, there is an equal and opposite reaction. Here, the table exerts a force of 5 N upward on the book. Therefore, the book must exert an equal and opposite force of 5 N downward on the table.

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: 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: 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 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: Contact Forces and Muscular Force

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

Key Concept: 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: 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, 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

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: Friction

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

Key Concept: Friction

c) It slows down and stops due to friction
[Solution Description]
Friction acts opposite to the direction of motion, slowing down the bicycle. When pedaling stops, friction causes the bicycle to decelerate and eventually come to rest.

Key Concept: Muscular Force, Friction

b) 53 N
[Solution Description]
First, calculate the frictional force:
$F_{\text{friction}} = \mu \times N$
Here, $N$ is the normal force which equals the weight $W = m \times g$. Assume $g = 9.8 \, \text{m/s}^2$:
$W = 50 \times 9.8 = 490 \, \text{N}$
$F_{\text{friction}} = 0.3 \times 490 = 147 \, \text{N}$
The applied muscular force is 200 N forward, and friction opposes it with 147 N backward:
$F_{\text{net}} = 200 – 147 = 53 \, \text{N}$
So, the net force acting on the sled is 53 N.

Key Concept: 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

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, 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: Muscular Force

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

Key Concept: Direction of Frictional Force

c) Opposite to the direction of motion.
[Solution Description]
Frictional force always opposes the relative motion between two surfaces in contact. When a book slides across a table, the frictional force acts opposite to the direction of the book’s motion.

Key Concept: Basic Concept: 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: 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: Friction, Motion Through Fluids, Conceptual Complexity

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

Key Concept: 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: 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: Electrostatic force, Magnetic force

d) Only electrostatic force can attract neutral objects temporarily
[Solution Description]
The electrostatic force attracts neutral paper pieces through polarization (induced dipoles), while magnetic attraction occurs between permanent or induced magnetic domains. The key difference is that electrostatic attraction can occur between a charged and neutral object through charge separation, whereas magnetic attraction requires magnetic properties in both objects or induced magnetism in ferromagnetic materials.

Key Concept: Magnetic force, Electrostatic force

a) Both forces originate from the same physical phenomenon but act on different materials
[Solution Description]
Magnetic force acts between magnetic materials or magnets due to alignment of magnetic domains, while electrostatic force arises from the transfer of electrons during friction. Unlike magnetic poles always attract, whereas similarly charged objects always repel. The key difference is their origin: magnetic force is due to dipole interactions, whereas electrostatic force results from excess or deficit of electrons.

Key Concept: Magnetic force definition

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

Key Concept: Magnetic Force

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 – 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: 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: 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 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: 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: Weight Unit

b) Newton
[Solution Description]
Weight, being a force, is measured in newtons ($N$). This is part of the International System of Units (SI).

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: Gravitational Force

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The Assertion states that the weight of an object on the Moon is less than its weight on Earth, which is true because the Moon’s gravity is about 1/6th of Earth’s gravity. The Reason correctly explains this by stating that the Moon exerts a weaker gravitational force compared to Earth. Therefore, both the Assertion and Reason are true, and the Reason correctly explains the Assertion.

Key Concept: 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: 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, which is correct because weight is a type of force (gravitational force) and the SI unit of force is newton (N). The Reason explains this correctly by mentioning that weight is the gravitational force acting on an object, and force is indeed measured in newtons. Therefore, both the Assertion and Reason are true, and the Reason correctly explains the Assertion.

Key Concept: Weight 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: Mass vs. Weight

b) 1 kg
[Solution Description]
From the table, 1 kg mass corresponds to 25.4 N on Jupiter. Therefore, an object weighing 25.4 N has a mass of 1 kg since weight is directly proportional to mass under the same gravitational force.

Key Concept: Weight Measurement

a) 3.6 N
[Solution Description]
The smallest division indicates 0.2 N, so three small divisions correspond to $0.2\,N \times 3 = 0.6\,N$. Adding this to the previous big mark (3 N), the total weight is $3\,N + 0.6\,N = 3.6\,N$.

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: 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: 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 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: Assertion-Reason

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

Key Concept: Difference between weight and mass

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: 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: 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: 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: Measurement of weight using a spring balance

b) 367 g
[Solution Description]
Weight ($W$) is related to mass ($m$) by the formula $W = mg$. Rearranged for mass, $m = \frac{W}{g}$. Substituting the values, $m = \frac{3.6 \, \text{N}}{9.8 \, \text{m/s}^2} \approx 0.367 \, \text{kg}$. To convert kg to grams, multiply by 1000: $0.367 \times 1000 = 367 \, \text{g}$.

Key Concept:

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: Assertion-Reason

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The Assertion states that an iron ship floats while an iron nail sinks. This is true because the ship’s design allows it to displace a large volume of water, making the buoyant force ($F_{buoyant} = \rho_{water} \times V_{displaced} \times g$) equal to its weight, enabling it to float (Archimedes’ Principle). The Reason explains that the buoyant force equals the weight of displaced water for the ship but is insufficient for the nail, causing it to sink. Both statements are correct, and the Reason logically explains the Assertion.

Key Concept:

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: 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: 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: 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: 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: Density and Floating

c) It has lower density than water
[Solution Description]
Pumice stone floats because it has a lower density than water. It contains tiny air pockets trapped inside during volcanic eruptions, making it porous and lighter than water. Hence, it displaces enough water to create a buoyant force equal to its own weight, allowing it to float.

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: Floating Condition

b) Sink because the weight exceeds the buoyant force
[Solution Description]
According to Archimedes’ Principle, an object will float if its weight is less than or equal to the buoyant force (weight of displaced fluid). Here, the object’s weight (500 N) is greater than the buoyant force (400 N). Thus, the object will sink.

Key Concept: Buoyant Force Calculation

c) 200 N
[Solution Description]
The buoyant force is calculated using Archimedes’ Principle:
$\text{Buoyant Force} = \text{Weight of displaced fluid}.$
First, find the mass of the displaced water:
$\text{Mass} = \text{Density} \times \text{Volume} = 1000 \text{ kg/m}^3 \times 0.02 \text{ m}^3 = 20 \text{ kg}.$
Now, calculate the weight of the displaced water:
$\text{Weight} = \text{Mass} \times g = 20 \text{ kg} \times 10 \text{ m/s}^2 = 200 \text{ N}.$
Therefore, the buoyant force is 200 N.