Explanation

In a reversible adiabatic process, there is no heat transfer (Q = 0).

As a result, the entropy change (ΔS) is zero because entropy change is directly related to heat transfer in a reversible process (ΔS = Q / T).

Explanation

The speed at a banked turn is given by:

v = √(rg tan(θ))

Given v = √(rg), we can equate:

√(rg tan(θ)) = √(rg)

This simplifies to:

tan(θ) = 1

θ = arctan(1) = 45°.

Explanation

The relation between alpha (α) and beta (β) is given by:

β = α / (1 - α)

Given α = 1/2:

β = (1/2) / (1 - 1/2)

= (1/2) / (1/2)

= 1

Explanation

For the X and Y components of a force to be equal:

Fx = Fy

Given F = Fx i + Fy j = F cos(θ) i + F sin(θ) j

Fx = F cos(θ)

Fy = F sin(θ)

For Fx = Fy:

F cos(θ) = F sin(θ)

cos(θ) = sin(θ)

tan(θ) = 1

θ = 45°

Explanation

The orbital speed (v) of a satellite is given by:

v = √(GM / (R + h))

If the orbital radius (R + h) is halved:

v' = √(GM / ((R + h) / 2))

= √(2GM / (R + h))

= √2 * √(GM / (R + h))

= √2 * v

So, the orbital speed will increase √2 times.

Explanation

The relation between the coefficient of volume expansion (γ) and the coefficient of linear expansion (α) is: γ = 3α

This relation holds true for isotropic solids.

The coefficient of volume expansion is approximately three times the coefficient of linear expansion.

Explanation

The turns ratio of a transformer is given by:

n = N₂ / N₁ = V₂ / V₁

Where:

- n is the turns ratio

- N₁ and N₂ are the number of turns in the primary and secondary coils

- V₁ and V₂ are the primary and secondary voltages

Given n = 5:

V₂ / V₁ = 5

This means the secondary voltage is greater than the primary voltage by a factor of 5.

Explanation

To find the pressure, we use the formula:

P = F / A

Where:

- P is the pressure

- F is the force (weight) = 392 N

- A is the area = 0.0001 m²

P = 392 N / 0.0001 m² = 3,920,000 Pa

To convert Pascals (Pa) to Megapascals (MPa):

3,920,000 Pa = 3.92 MPa

Explanation

The energy density (u) in a capacitor is given by:

u = ½ε₀E²

Where:

- ε₀ is the permittivity of free space

- E is the electric field intensity between the plates

This shows that the energy density is proportional to the square of the electric field intensity (E²).

Explanation

The relation between work (W) done and torque (τ) in rotational motion is:

W = τdθ

Where:

- W is the work done

- τ is the torque

- dθ is the angular displacement

This shows that work done in rotational motion is the product of torque and angular displacement.