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.

Explanation

e/m = 2E/B²r²

The formula is derived by equating the magnetic Lorentz force to the centripetal force and using the kinetic energy gained from the accelerating voltage E.

This formula correctly relates the charge-to-mass ratio of an electron to the magnetic field B, radius of the circular path r, and accelerating voltage E.

Explanation

For a polyatomic gas, Cv is typically 3R, accounting for translational and rotational degrees of freedom.

This value can increase with temperature as vibrational modes become excited, contributing to the specific heat.

Explanation

When an object is placed at the principal focus (F) of a convex lens, the rays emerge parallel after refraction.

Parallel rays appear to meet at infinity, so the image is formed at infinity (very far away).

Explanation

Given:

Magnification M = 5

Distance between lenses L = f₀ + fₑ = 24 cm

Magnification formula M = f₀ / fₑ

Let's solve for f₀ and fₑ:

1. f₀ / fₑ = 5 => f₀ = 5fₑ

2. f₀ + fₑ = 24

Substituting f₀ = 5fₑ into the second equation:

5fₑ + fₑ = 24

6fₑ = 24

fₑ = 4 cm

Now, f₀ = 5fₑ = 5 × 4 = 20 cm

Explanation

The equation of continuity A₁V₁ = A₂V₂ represents the conservation of mass in fluid flow.

The constant is equal to the Volume flow rate, which is the volume of fluid passing through a given area per unit time.

Explanation

If the original cable breaks at a stretch of 2 mm, each half will have half the length and thus half the maximum stretch:

Maximum stretch for half = 2 mm / 2 = 1 mm.

Explanation

The energy equivalent of 1 atomic mass unit (a.m.u) is given by Einstein's mass-energy equivalence formula E = mc².

1 a.m.u = 931 MeV/c², so the energy equivalent is 931 MeV.

Explanation

Time = Energy / Power

Given Energy = 1.4 × 10⁶ J and Power = 2 kW = 2000 W:

Time = (1.4 × 10⁶ J) / (2000 W)

Time = 1.4 × 10⁶ / 2000

= 700 s