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 and Interaction

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that when a football player kicks a ball, the ball moves in the direction of the kick. This is true because applying a force (kick) causes the ball to move. The reason states that a force is a push or pull resulting from the interaction between two objects, which is also true as per the definition of force. Moreover, the reason correctly explains why the ball moves—because the player's foot interacts with the ball, applying a force that sets it in motion.

Key Concept: 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: 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) A person lifting a heavy bag
[Solution Description]
Muscular force is the force exerted by muscles when they contract or elongate. Lifting a bag involves the use of arm muscles to apply an upward pull, making it a clear example of muscular force. The other options involve non-muscular forces like magnetic or gravitational forces.

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: 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: 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: Force effects, Multiple concepts

c) Both speed and direction change gradually
[Solution Description]
Analysis: 1) Initial rolling has kinetic energy (eastward). 2) Kick applies new force vector northward. 3) First effect: eastward motion decreases (force opposes original direction). 4) Second effect: northward motion increases. 5) Net result: direction changes northeast briefly, then north as east component vanishes. This shows multiple force effects simultaneously.

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: 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: Effect of Force on Motion

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that when a cyclist stops pedaling on a smooth downhill slope, the bicycle continues to move with increasing speed. This is true because gravity pulls the bicycle downward along the slope, accelerating it. The reason claims that the gravitational force acts in the direction of motion, causing the bicycle to accelerate. This is also true and correctly explains why the assertion occurs. Gravitational force is indeed the reason for the bicycle's acceleration downhill.

Key Concept: 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: 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: Types of Forces

c) Muscular force
[Solution Description]
The act of lifting involves muscular force, which is exerted by living beings using their muscles. In this case, the child uses muscular force to lift the school bag.

Key Concept: 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 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: 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: Change in Shape Due to Force

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

Key Concept: Effects of Force

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: Effect of Force

b) The ball changes its direction.
[Solution Description]
Hitting a moving ball with a bat applies a force to the ball. This force changes the direction of the ball's motion, as seen in sports like cricket or baseball.

Key Concept: Effect of force, Change in shape

c) The rubber band changes its shape but does not accelerate
[Solution Description]
Step 1: The rubber band is subjected to two equal and opposite forces (10 N each).
Step 2: Since the forces are balanced (net force is zero), there is no change in the state of motion of the rubber band.
Step 3: However, the rubber band stretches because the applied forces cause its shape to change.
Thus, the primary effect here is a change in shape without any net acceleration.

Key Concept: Effect of Force

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: 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: 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: Forces as Interaction

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that a force cannot exist if only one object is present, which is true because forces require interaction between two or more objects, as mentioned in the syllabus. The reason correctly explains why the assertion is true: forces arise due to interaction between at least two objects. Thus, both are true, and the reason correctly explains the assertion.

Key Concept: Force and Interaction

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that a force is a push or pull resulting from interaction, which is true as per the syllabus definition of force. The reason states forces arise only when two objects interact, which is also true and directly explains why forces are interactions between objects. Hence, both are true, and the reason correctly explains the assertion.

Key Concept: Unbalanced forces, Acceleration

b) \(2\,\mathrm{m/s^2}\)
[Solution Description]
First, find the net force acting on the object: 6 N (right) - 2 N (left) = 4 N to the right. Using Newton's Second Law ($F = ma$), we can calculate the acceleration: $a = F/m = 4 N / 2 kg = 2 m/s^2$.

Key Concept: 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: Definition of Force

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

Key Concept: Balanced 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

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

Key Concept: Force Interaction, SI Unit of Force

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

Key Concept: Force interaction, Balanced forces

d) All forces acting on the car are balanced
[Solution Description]
When an object moves with constant velocity, the net force acting on it is zero. This means all the forces acting on the car are balanced - i.e., the driving force equals the opposing frictional forces.

Key Concept: Force as Interaction

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, 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 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: 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: 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 and Non-Contact Forces

c) Magnetic force
[Solution Description]
Non-contact forces are those that act between objects without any physical contact. Examples include magnetic force, electrostatic force, and gravitational force. Muscular force is a contact force, while frictional force also requires contact.

Key Concept: Muscular force, Gravitational force

c) Both contact and non-contact forces act in opposite directions
[Solution Description]
The weightlifter applies muscular force to lift the barbell. The gravitational force acts downward with magnitude F = mg = 100 kg × 9.8 m/s$^2$ = 980 N. The upward muscular force must overcome this gravitational force. The calculation shows both contact (muscular) and non-contact (gravitational) forces are involved.

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: Muscular Force

c) Muscular force
[Solution Description]
When a person lifts a box, the force is generated by the contraction and elongation of muscles in their body. This is called muscular force, which is a type of contact force as it requires direct or indirect physical contact.

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: 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: 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: 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: 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

c) It arises from muscle contractions.
[Solution Description]
Muscular force is a type of contact force that occurs due to the contraction and elongation of muscles. It is used in activities like lifting, pushing, or running, where physical contact is necessary.

Key Concept: Muscular Force Applications

c) By contracting and relaxing muscles to move food
[Solution Description]
Muscular force helps in digestion by contracting and relaxing muscles to chew food and push it through the alimentary canal. This mechanical process aids in breaking down food for nutrient absorption.

Key Concept: Muscular Force

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: Basic Concept: Direction of Friction

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

Key Concept: 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, 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: Friction, Surface Irregularities, Real-World Application

b) 20 N
[Solution Description]
To move the block, the applied force must overcome the static friction. The formula for maximum static friction is $f_s = \mu_s \times N$, where $\mu_s$ is the coefficient of static friction and $N$ is the normal force. Here, the normal force equals the weight of the block, i.e., $N = 50\, \text{N}$. Substituting $\mu_s = 0.4$, we get $f_s = 0.4 \times 50 = 20\, \text{N}$. Thus, the minimum force required to start moving the block is 20 N.

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: Gravitational force, Non-contact forces

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

Key Concept: Magnetic force, 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: 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: Poles interaction

b) They repel each other
[Solution Description]
When like poles (North-North or South-South) of two magnets are brought close, they repel each other due to the nature of magnetic forces.

Key Concept: Magnetic force, Non-contact forces

a) The Earth's magnetic South pole is located at the geographic North pole
[Solution Description]
The Earth acts like a giant magnet with its magnetic South pole near the geographic North pole. A compass needle aligns itself along the Earth's magnetic field lines. The North-seeking pole of the compass needle is attracted to the Earth's magnetic South pole, which is why it points towards the geographic North pole.

Key Concept: Magnetic force, Non-contact forces

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

Key Concept: Magnetic Force - Non-contact nature

b) It can act over a distance without physical contact
[Solution Description]
Magnetic force acts over a distance without requiring any physical contact between the interacting objects. This characteristic classifies it as a non-contact force.

Key Concept: 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: 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: Attraction

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

Key Concept: Electrostatic force: Force between charged objects

c) Assertion is true, but Reason is false.
[Solution Description]
The assertion states that when two balloons are rubbed with a woollen cloth and released, they repel each other. This is true because rubbing the balloons transfers electrons, making them similarly charged. According to Coulomb's Law ($F = k \frac{q_1 q_2}{r^2}$), like charges repel each other. However, the reason given is "Like charges attract each other," which is false because like charges repel, not attract. Therefore, the assertion is true, but the reason is false.

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 Variation Across Planets

c) 19 N
[Solution Description]
First, find the mass of the object using the known weight on Earth:
$W = m \times g_{\text{Earth}} \\ \\ 50 = m \times 10 \\ \\ m = 5 \text{ kg}$
Now, calculate its weight on Mars using Mars' gravity:
$W_{\text{Mars}} = m \times g_{\text{Mars}} \\ \\ W_{\text{Mars}} = 5 \times 3.8 = 19 \text{ N}$
Thus, the object's weight on Mars is approximately 19 N.

Key Concept: 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, Weight, Non-contact force

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.
[Solution Description]
The Assertion states that the weight of an object on the Moon is less than its weight on Earth due to the weaker gravitational force of the Moon. This is true because the table in the syllabus shows the weight of a $1 \, kg$ object is $1.6 \, N$ on the Moon compared to $10 \, N$ on Earth. The Reason states that gravitational force is a non-contact force and varies with the mass of the celestial body. This is also true as gravitational force acts without contact and differs based on the mass of the planet or moon (e.g., Jupiter's gravitational force is much stronger). However, the Reason does not directly explain why the Moon’s gravitational force is weaker; it merely states facts about gravitational force. Thus, both statements are true, but the Reason is not the correct explanation of the Assertion.

Key Concept: 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 Measurement

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

Key Concept: 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 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: 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: Gravitational Force Calculation

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

Key Concept: Weight Measurement and Gravitational Force

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

Key Concept: Difference between 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: 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: Mass vs. Weight

c) Mass remains constant, but weight changes depending on the gravitational field.
[Solution Description]
Mass is the amount of matter in an object and remains constant regardless of location. Weight is the gravitational force acting on the object, which varies with the gravitational field strength. The SI unit of mass is kilogram ($\text{kg}$), while the SI unit of weight is newton ($\text{N}$).

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: 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

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 using a spring balance

c) 0.1 N
[Solution Description]
The difference between two major marks is 0.5 N (since there are 10 divisions from 0 N to 5 N: $\frac{5 \, \text{N}}{10} = 0.5 \, \text{N}$). Each major division has 5 smaller divisions, so the smallest division represents $\frac{0.5 \, \text{N}}{5} = 0.1 \, \text{N}$. Hence, the smallest weight measurable is 0.1 N.

Key Concept: Spring Balance Maximum Weight

b) 10 N
[Solution Description]
The maximum weight a spring balance can measure is given by its upper limit, which is explicitly stated as 10 N.

Key Concept: Volume Displacement, Multiple Fluids

c) $\rho_s = 0.4\rho_1 + 0.5\rho_2$
[Solution Description]
Using Archimedes' principle for equilibrium:
Weight of sphere = Total buoyant force
$\rho_s V g = \rho_1 (0.4V) g + \rho_2 (0.5V) g$
Cancel $Vg$ from all terms:
$\rho_s = 0.4\rho_1 + 0.5\rho_2$
Remaining 10% is above the interface

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:

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

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: 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, Floating condition

b) 20%
[Solution Description]
First, find the volume of the block: $V = \frac{m}{\rho_s} = \frac{2}{800} = 0.0025$ m$^3$.
When floating, the buoyant force equals the block's weight: $\rho_l \cdot V_{\text{submerged}} \cdot g = m \cdot g$.
Substituting values: $1000 \cdot V_{\text{submerged}} = 2$.
Thus, $V_{\text{submerged}} = 0.002$ m$^3$.
The fraction submerged is $\frac{V_{\text{submerged}}}{V} = \frac{0.002}{0.0025} = 0.8$.
Therefore, the fraction above water is $1 - 0.8 = 0.2$ or 20%.

Key Concept: Buoyant Force and Density

b) 400 kg/m$^3$
[Solution Description]
According to Archimedes' Principle, the buoyant force equals the weight of the displaced liquid. Since the block floats, the weight of the block equals the buoyant force.
Let the volume of the block be $V$ and its density be $\rho_b$. The volume of displaced liquid is $\frac{V}{2}$.
Weight of the block: $W_b = \rho_b \times V \times g$
Weight of displaced liquid: $W_l = \rho_l \times \frac{V}{2} \times g$
Since $W_b = W_l$:
$\rho_b \times V \times g = 800 \times \frac{V}{2} \times g$
Simplifying:
$\rho_b = \frac{800}{2} = 400 \, \text{kg/m}^3$

Key Concept: Upthrust or buoyant force

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The Assertion is true because the buoyant force reduces the apparent weight of the submerged mug, making it feel lighter. The Reason is also true as it correctly explains the cause of the buoyant force according to Archimedes' Principle, which states that the buoyant force equals the weight of the displaced liquid. Therefore, both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

Key Concept: Buoyant Force

c) Buoyant force is equal to the weight
[Solution Description]
When an object floats, it means the buoyant force equals the object's weight. This balance allows the object to stay afloat without sinking or rising further. So, if an object is floating, the buoyant force is equal to its weight.

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

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: 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.