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Concept:

• Transformer: An electrical device that is used to transfer electrical energy from one electrical circuit to another is called a transformer.

There are two types of transformers:

• Step-up transformer: The transformer which increases the potential is called a step-up transformer.
• The number of turns in the secondary coil is more than that in the primary coil.
• Step-down transformer: The transformer which decreases the potential is called a step-down transformer.
• The number of turns in the secondary coil is less than that in the primary coil.

Explanation:

• In a transformer, primary volt-ampere is equal to secondary volt-ampere and primary ampere-turns are also equal to secondary ampere-turns.
• So, EMF per turn in both windings is equal. Total induced emf on both sides depends on the number of turns, flux, and frequency.
• If the number of turns on the secondary is more than the primary, then the emf induced in the secondary will be more than the primary side and vice versa, but the emf per turn in both the windings is equal.

​V₁ I₁ = ​V₂ I₂

N₁I1 = N₂I2 

 ∴\(\frac{{{E_1}}}{{{N_1}}} = \frac{{{E_2}}}{{{N_2}}}\)

CONCEPT:

• The process of increasing the volume of sound with the help of an amplifier is called amplifications.
• Extracting the original information-bearing signal from a carrier wave is called Demodulation.
• The process of transmitting the signal wave from one place to another is called transmission.
• The process of super imposing message signal on carrier wave is called modulation.

EXPLANATION:

• Since the extracting the original information-bearing signal from a carrier wave is called Demodulation. So option 2 is correct.

CONCEPT:

• Compression: Compression is a region in a longitudinal wave where the particles are closest together.
• Compression has high density and high pressure
• Rarefaction: A rarefaction is a region in a longitudinal wave where the particles are furthest apart.
• Rarefaction has a low density and low pressure

EXPLANATION:

• In the propagation of sound compression is region of high density and high pressure. So option 1 is correct.

The correct answer is 25 N.

Key Points

To find the amount of force needed to accelerate a mass, we use Newton's second law of motion, which states: \(\rm F= ma\)

Where:

• F is the force,
• m is the mass,
• a is the acceleration.

Given:

• \(\rm m = 10 kg\),
• \(\rm a= 2.5 m/s^2\),

We can calculate F as follows:

\(\rm F=10 Kg \times 2.5 m/s^2= 25N\)

Therefore, the force needed is 25 N.

Additional Information

• Force:
• Force is an interaction that, when unopposed, will change the motion of an object.
• A force can cause an object with mass to change its velocity (which includes to begin moving from a state of rest), i.e., to accelerate.
• Force is a vector quantity, meaning it has both magnitude and direction.
• Newton's Second Law of Motion:
• It states that the force acting on an object is equal to the mass of the object times its acceleration (\(\rm F= ma\)).
• This law explains how the velocity of an object changes when it is subjected to an external force.
• Mass:
• Mass is a property of a physical body and a measure of its resistance to acceleration when a force is applied.
• The mass of an object also determines the strength of its gravitational attraction to other bodies.
• Acceleration:
• Acceleration is the rate of change in the velocity of an object with respect to time.
• It is a vector quantity, meaning it has both magnitude and direction.

The correct answer is option 2) i.e. the linear momentum of the system

CONCEPT:

• Linear momentum: Momentum is defined as the impact due to a moving object.
• Linear momentum, p = mv

Where m is the mass of the object and v is the velocity of the object.

EXPLANATION:

Let us consider a system of particles with each particle having a mass  m and velocity v.

If p is the linear momentum od each particle, p = mv

Total linear momentum, Σp = Σmv = Σm . Σv = M.v_com

Where M is the sum of mass of all particles, and v_com is the velocity of the centre of mass.

The vector addition of velocities will give a net velocity with respect to the centre of mass.

Hence, the linear momentum of a system = product of the total mass of a system and the velocity of the centre of mass

CONCEPT**:**

• Angular Momentum (L): It is a property of a body in rotational motion.
• The moment of linear momentum is known as angular momentum.

L = r × p = r × mv

where p is the momentum of the body, r is the distance of linear momentum from the axis of rotation, m is the mass of the body, and v is the velocity of the body.

• Linear momentum Conservation: When in a system, there is no external force then the total momentum (P) of the system will be conserved.
• Angular momentum Conservation: When in a system, there is no external torque then the total angular momentum (L) of the system will be conserved.

EXPLANATION**:**

• If net external torque on a rotating object is zero, Its angular momentum will be conserved i.e. will be constant.
• Linear momentum is conserved when there is no external force on the body.
• Linear velocity is constant when a body is moving with a constant speed and constant direction.
• The angular velocity of a body is constant if it is moving in a uniform circular motion.
• So the correct answer is option 4.

CONCEPT:

• A rectangular coil always acts as a magnetic dipole of dipole moment M.
• The dipole moment of a rectangular coil is given by:
• The dipole moment of the coil (M) = N I A

Where N is the number of turns, I is current in the coil and A is the area of the rectangular coil

• The torque of the magnetic field on any magnetic dipole moment is given by;

⇒ T = M × B = MB Sinθ

Where M × B = cross product of Area vector A and magnetic field vector B and θ = the angle between area vector A and magnetic field B.

EXPLANATION:

• The dipole moment of the coil is

⇒ M = N I A

Torque on rectangular coil (T) = M × B = MB Sinθ = N I A B Sinθ

• According to the above formula of the torque on a rectangular coil in a magnetic field, torque will be large when the number of turns is large. So option 1 is correct and option 2 is wrong.
• If the magnetic field is perpendicular to the plane of the coil then it will be along the area vector. So the angle between the area vector and the magnetic field will be zero and finally, the torque will be zero. So option 3 is wrong.
• If the area will be small then torques will also be small. So option 4 is wrong.

The correct answer is Kelvin.

Key Points

• The Kelvin scale is an absolute temperature scale starting at absolute zero, the point where all molecular motion ceases.
• Absolute zero is defined as 0 K on the Kelvin scale, which is equivalent to -273.15°C on the Celsius scale.
• Since the Kelvin scale starts from absolute zero, it does not have negative values.
• The Kelvin scale is primarily used in scientific contexts, especially in physics and chemistry, due to its absolute nature.
• The Kelvin scale is named after William Thomson, 1^st Baron Kelvin, who proposed it in the mid-19^th century.

Additional Information

• Reaumur Scale
• The Reaumur scale, also known as the "octogesimal division," has its freezing point of water at 0 degrees and the boiling point of water at 80 degrees.
• It is not commonly used today and has been largely replaced by the Celsius and Kelvin scales.
• Fahrenheit Scale
• The Fahrenheit scale, used primarily in the United States, sets the freezing point of water at 32 degrees and the boiling point at 212 degrees.
• This scale can have negative values; for instance, the freezing point of brine is 0°F, which is lower than the freezing point of water.
• Celsius Scale
• The Celsius scale sets the freezing point of water at 0 degrees and the boiling point at 100 degrees under standard atmospheric pressure.
• It can have negative values, for example, temperatures below the freezing point of water.
• Temperature Scales Comparison
• The Kelvin scale is used in scientific measurements where absolute values are necessary.
• The Celsius scale is widely used around the world in everyday temperature measurements.
• The Fahrenheit scale is used primarily in the United States for everyday temperature measurements.

The correct answer is option 4) i.e. All of the above

CONCEPT:

• Law of Universal Gravitation: It states that all objects attract each other with a force that is proportional to the masses of two objects and inversely proportional to the square of the distance that separates their centres.

It is given mathematically as follows:

\(F = \frac{Gm_1m_2}{R^2}\)

Where m1 and m2 are the mass of two objects, G is the gravitational constant and R is the distance between their centres.

• The gravitational force acting on an object of mass m placed on the surface of Earth is:

\(F = \frac{GMm}{R^2}\)

Where R is the radius of the earth. 

• From Newton's second law, F = ma = mg

⇒ mg = \(\frac{GMm}{R^2}\)

Therefore, acceleration due to gravity, g = \(\frac{GM}{R^2}\)

• The Earth is shaped like an ellipsoid where the region around the equator bulges outwards more as compared to the poles.

EXPLANATION:

• Acceleration due to gravity, g = \(\frac{GM}{R^2}\)
• At the centre of the earth, R = 0. Therefore, g = zero.
• Since the equator is bulged outwards as compared to the poles, the radius of the earth decreases as we move from the equator to the poles. Therefore, gravity increases from the equator to the poles.
• Acceleration due to gravity of an object is independent of its mass as g only depends on the mass of the earth (M) and the radius of the earth (R).​

​Hence**, all the given statements are correct.**

The correct answer is 10 B.

Key Points

• The magnetic field (B) created by a coil is directly proportional to the number of turns (N) in the coil.
• If a single-turn coil produces a magnetic field B, then a coil with 10 turns will produce a magnetic field proportional to 10 times the single-turn coil.
• The relationship can be expressed as B_{10 turns} = N * B_{single turn}, where N is the number of turns.
• Therefore, for 10 turns, the magnetic field B_{10 turns} = 10 * B.
• Hence, the magnetic field due to a circular coil with 10 turns will be 10 B.

Additional Information

• Magnetic Field:
• It is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials.
• The symbol for the magnetic field is B, and it is measured in teslas (T).
• Electromagnetic Induction:
• It is the production of an electromotive force (EMF) across an electrical conductor in a changing magnetic field.
• This principle is fundamental in the operation of transformers, inductors, and many types of electrical generators and motors.
• Right-Hand Rule:
• It is a mnemonic for understanding the direction of the magnetic field relative to the direction of the current.
• If you point your thumb in the direction of the current, the curl of your fingers shows the direction of the magnetic field loops.
• Solenoid:
• A solenoid is a coil wound into a tightly packed helix, which generates a magnetic field when an electric current passes through it.
• The magnetic field inside a solenoid is uniform and parallel to the axis of the solenoid.