The velocity is maximum at the mean position where the displacement is zero.

Maximum speed (v_max) = ωA. Thus, ω = v_max/A = 4/2 = 2 rad/s.

As the slit width decreases, the central maximum becomes wider due to increased diffraction.

The intensity of the central maximum is four times that of the first minimum in a single-slit diffraction pattern.

The intensity at the first minimum is zero, while the central maximum has maximum intensity.

The width of the central maximum is inversely proportional to the slit width. Halving the slit width doubles the width of the central maximum to 8 mm.

For single-slit diffraction, the first minimum occurs at sin θ = λ/a. Here, sin θ = 600 x 10^-9 m / 0.5 x 10^-3 m = 0.0012, θ ≈ 0.0698 rad ≈ 4°.

The angle for the first minimum in single-slit diffraction is given by sin(θ) = λ/a, where a is the slit width.

The first minimum in a single-slit diffraction pattern occurs at sin(θ) = λ/a, where a is the width of the slit.

Angular width = 2λ/a. Here, a = 0.5 mm = 500 μm, so angular width = 2 * 500 nm / 500 μm = 0.002 rad = 0.2 rad.

The first minimum in a single-slit diffraction pattern occurs at θ = λ/a, where a is the width of the slit.

Two parallel wires carrying currents in the same direction experience an attractive force between them.

The magnetic field inside a solenoid is directed from the north pole to the south pole of the solenoid.

The magnetic field inside a solenoid is uniform and directed along the axis of the solenoid.

The magnetic field inside a solenoid carrying current is given by B = μ₀nI, where n is the number of turns per unit length.

The magnetic field inside a solenoid is directly proportional to the number of turns per unit length, so it doubles.

The length of the solenoid does not affect the strength of the magnetic field inside it; it is determined by the number of turns per unit length, the current, and the permeability of the core material.

Increasing the number of turns per unit length in a solenoid increases the magnetic field strength.

Inside a long solenoid, the magnetic field is given by B = μ₀nI, where n is the number of turns per unit length.

Mole fraction of solute = moles of solute / (moles of solute + moles of solvent) = 1 / (1 + 9) = 0.1.

Mole fraction of A = moles of A / (moles of A + moles of B) = 3 / (3 + 1) = 0.75.

The addition of a non-volatile solute raises the boiling point of the solvent, a phenomenon known as boiling point elevation.

The presence of a non-volatile solute lowers the vapor pressure of the solvent compared to that of the pure solvent.

Using Raoult's Law, the vapor pressure of the solution is P_total = (0.6 * 100) + (0.4 * 50) = 60 + 20 = 80 mmHg.

The total vapor pressure of a solution is the sum of the partial vapor pressures of its components: 80 mmHg + 20 mmHg = 100 mmHg.

For a spontaneous process, the change in Gibbs free energy (ΔG) is negative.

In a standing wave, the points of maximum displacement are called antinodes, while nodes are points of zero displacement.

The distance between two consecutive nodes in a standing wave is λ/2.

A node is a point in a standing wave where the displacement is always zero.

Nodes in a standing wave are points where there is no displacement, meaning they are points of minimum amplitude.