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Calculation:

From Newton's law:

F = G × (m₁ × m₂) / r²

Rearranging for G:

G = F × r² / (m₁ × m₂)

⇒ F (N) = kg × m/s², r² = m², m₁, m₂ = kg

⇒ G = (kg × m/s²) × m² / (kg × kg)

⇒ G = N · m² / kg²

∴ The SI unit of G is N · m² / kg².

Concept Used:

When two objects are in free fall (ignoring air resistance), their motion is governed by the force of gravity. The following points are relevant:

Acceleration: All objects experience the same acceleration due to gravity (g = 9.8 m/s²) regardless of their mass.

Momentum: Momentum (p) = mass × velocity. Since the bodies have different masses, their momenta will differ.

Kinetic Energy: KE = (1/2) × mass × velocity². As mass differs, so does kinetic energy.

Potential Energy: PE = mass × g × height. Again, different masses result in different potential energies.

∴ The only quantity equal for both bodies is acceleration.

∴ The correct answer is Option 2: Acceleration.

CONCEPT:

Wave: It can be defined as the transport of energy without the transport of matter.

The properties of waves are:

Wavelength (λ): The distance between two crests or troughs of a wave is known as wavelength. One wavelength equals the distance between two consecutive crests.

Frequency (f): The number of oscillations or the number of waves passes a given point in one sec. Its SI unit is Hertz.

Time period (T): The time taken by the wave to complete one cycle.

The relation between velocity, wavelength, and frequency of a wave is

⇒ v = λ × f 

That is, speed = wavelength × frequency

Calculation:

Initial time period, T_old = 2π√(L / g)

New time period, T_new = 2π√(4L / g)

⇒ T_new = 2π√(4)√(L / g)

⇒ T_new = 2 × 2π√(L / g)

⇒ T_new = 2T_old

⇒ T_new : T_old = 2 : 1

∴ The ratio of the new and previous time period is 2:1.

Concept:

Electric charge is a fundamental property of matter responsible for electric forces and interactions.

Key properties of electric charge include:

Conservation of charge: The total charge in an isolated system is constant.

Quantization of charge: The charge on a body is always an integral multiple of the elementary charge (e).

Superposition principle: Charges can be added algebraically to find the net charge.

Charge invariance: Charges cannot be created or destroyed in an isolated system.

∴ Option 4 is NOT a basic property of electric charge.

CONCEPT:

• Scattering of light: The phenomenon in which the light ray is redirected in all other directions on passing through particles of dimensions comparable to the wavelength of the light used is called scattering of light.
• Rayleigh scattering: The scattering of light off of the molecules of the air that can be extended to scattering from particles up to about a tenth of the wavelength of the light used is called Rayleigh scattering.

According to Rayleigh scattering:

Scattering \(\propto \frac{1}{{{\lambda ^4}}}\)

Where λ is the wavelength of light

For white light:

Order of wavelength:

Violet < Indigo < Blue < Green < Yellow < Orange < Red

EXPLANATION:

• According to the above, the scattering is inversely proportional to the fourth power of the wavelength of the light.
• As we know that in primary colour (blue, green, yellow, orange and red), the blue colour is having least wavelength and therefore scattered the most.
• The scattered light is the sky contains abundant blue light and therefore sky appears blue. So option 1 is correct.

CONCEPT:

• When a body is either wholly or partially immersed in a fluid, a lift is generated due to the net vertical component of hydrostatic pressure forces experienced by the body. This lift is called the buoyant force and the phenomenon is called buoyancy.
• The Archimedes principle states that the buoyant force on a submerged body is equal to the weight of the liquid displaced by the body and acts vertically upward through the centroid of the displaced volume.
• Thus, the net weight of the submerged body, (the net vertical downward force experienced by it) is reduced from its actual weight by an amount that equals the buoyant force FB.

⇒ FB = Vdisplaced, ρg

⇒ FB = f(Vdisplaced, ρ)

So, the correct answer is option 2.

Calculation:

Given:

The length of the copper wire is increased by twice.

Using the formula for resistivity: ρ = R × A / L

Resistivity (ρ) depends only on the material and is independent of changes to the length (L) or cross-sectional area (A).

⇒ Increasing the length of the wire does not affect resistivity.

∴ Resistivity remains the same.

The correct answer is Option 3: Same.

​Concept Used:

A dimensionless quantity is a physical quantity that has no physical dimensions and is expressed as a pure number.

To determine if a quantity is dimensionless, analyze its dimensional formula:

Stress: Force per unit area (F / A)

Dimensional Formula: [M¹ L^-1 T^-2]

Strain: Change in length / Original length (ΔL / L)

Dimensional Formula: Dimensionless (pure ratio)

Pressure: Force per unit area (F / A)

Dimensional Formula: [M¹ L^-1 T^-2]

Force: Mass × Acceleration

Dimensional Formula: [M¹ L¹ T^-2]

∴ The dimensionless quantity is Strain .

Explanation:

Adiabatic process:

• When a thermodynamic system undergoes a change in such a way that no exchange of heat takes place between Systems and surroundings, the process is known as an adiabatic process.
• During the adiabatic process, there is no exchange of heat that takes place between the system and surroundings.

i.e. ΔQ = 0.

Additional Information

• Isothermal process: When a thermodynamic system undergoes a physical change in such a way that its temperature remains constant, then the change is known as an isothermal process.
• Isobaric process: When a thermodynamic system undergoes a physical change in such a way that its pressure remains constant, then the change is known as the isobaric process.
• Isochoric process: When a thermodynamic process undergoes a physical change in such a way that its volume remains constant, then the change is known as the isochoric process.

Isentropic process: 

• In the Isentropic process, the state of entropy is constant.
• That is why it is also known as a constant-entropy process.
• This process is both reversible as well as adiabatic.
• In the adiabatic process, there is no transfer of heat or matter.
• It is an idealized thermodynamic process in thermodynamics.

Entropy: It is the measure of thermal energy of a system per unit temperature that is unavailable for doing useful work.

• In simple words entropy of the world keeps increasing because we move far away from equilibrium every second.