Explanation

Resistivity after cutting a wire in half:

Resistivity 𝜌 is a material property, independent of shape, size, or length.

When a wire is cut, resistance changes, but resistivity remains the same.

Explanation

 According to Gauss's Law, the net electric flux through a closed surface depends on the net charge enclosed.

If equal and opposite charges are present inside the surface, their total is zero, so the net electric flux is also zero.

Explanation

The electrostatic force between two charges is given by Coulomb’s Law:

F = k * q₁ * q₂ / R²

If a total charge Q is divided into two parts: q and Q−q, the force becomes:

F = k * q * (Q − q) / R²

To maximize F, differentiate F with respect to q and set dF/dq = 0:

dF/dq = k/R² * [Q − 2q] = 0  

⇒ Q − 2q = 0  

⇒ q = Q/2

Explanation

To convert Celsius to Kelvin, use the formula:

K = °C + 273.15

So,

K = 501.25 + 273.15 = 774.40 K

Explanation

The speed of sound in an ideal gas is proportional to √(P/ρ).  

But at constant temperature, P/ρ remains constant for gases (since both pressure and density scale equally).  

So, the velocity of sound is independent of pressure if temperature is constant.

Hence, ratio = 1:1.

Explanation

For a point source in 3D, amplitude is inversely proportional to the distance from the source:  

A ∝ 1/r  

So, if distance doubles (2r), amplitude becomes A/2.

Explanation

The device that can be used for precise measurement of wavelength is a Michelson Interferometer. 

A Michelson interferometer uses the interference of light waves to measure very small distances, including wavelengths, with high accuracy. 

Explanation

The correct answer is:  All of the above

A complete revolution corresponds to an angular displacement of:

• 360°

• $2\pi$ radians

So, for 2 complete revolutions:

• Degrees: $2\times 360°=720°$

• Radians: $2 times 2pi = 4pi$ radians

• Approximate radians:

  $$4\pi \approx 4\times 3.14=12.56\text{ radians (rounded to 12.6)}$$

Explanation

Rotational kinetic energy of a disc about its center:  

K.E = (1/2) I ω², where I = moment of inertia.

For a disc, I = (1/2)MR²,  

So, K.E = ½ × (½ MR²) × ω² = ¼ MR²ω²

If linear velocity v = Rω, then  

K.E = ¼ Mv²

Explanation

When a car moves at constant velocity, it means there is no acceleration.

According to Newton’s First Law, if there’s no acceleration, the net force acting on the object is zero.