Work done (W) = P * ΔV = 100 kPa * (2 m³ - 1 m³) = 100 kPa * 1 m³ = 100 kJ = 10 kJ.

Using Boyle's Law, P1V1 = P2V2, we find P2 = P1 * (V1/V2) = 1 atm * (4 L / 1 L) = 4 atm.

Total marbles = 4 + 5 + 1 = 10. Probability of yellow = 5/10 = 1/2.

According to the law of reflection, the angle of reflection is equal to the angle of incidence. Therefore, the angle of reflection is also 30 degrees.

Efficiency = (Output Work / Input Energy) * 100 = (1200 J / 2000 J) * 100 = 60%.

The period T is the reciprocal of frequency f. Thus, T = 1/f = 1/2 = 0.5 s.

Frequency f = 1/T = 1/2 s = 0.5 Hz.

At the top, T + mg = mv²/L. T = mv²/L - mg.

Angular frequency ω is related to frequency f by ω = 2πf. Therefore, for f = 1 Hz, ω = 2π(1) = 2π rad/s.

Angular frequency ω = 2πf = 2π × 5 Hz = 10π rad/s.

The maximum speed v_max is given by v_max = Aω, where A is the amplitude and ω is the angular frequency. Thus, v_max = 0.1 * 20 = 2 m/s.

Energy U = 1/2 C V^2. Initial U = 1/2 * 5 × 10^-6 * 10^2 = 0.025 J; Final U = 1/2 * 5 × 10^-6 * 20^2 = 0.1 J. Change = 0.1 - 0.025 = 0.075 J = 75 µJ.

Angular velocity ω = v/r.

Centripetal acceleration a_c = v²/r.

Frequency f = number of oscillations / time = 20 / 40 s = 0.5 Hz.

The potential energy of a pendulum is maximum at the highest point of its swing, where its kinetic energy is minimum.

For small angles, T ≈ 2π√(L/g). Assuming L = 1 m, T ≈ 2π√(1/9.8) ≈ 2.0 s.

Work = mgh = 10 kg * 9.8 m/s² * 2 m = 196 J.

Using Snell's law, n1 * sin(theta1) = n2 * sin(theta2). Here, n1 = 1 (air), theta1 = 45 degrees, n2 = 1.5 (glass). Thus, sin(theta2) = (1 * sin(45))/1.5 = 0.471, giving theta2 ≈ 30 degrees.

For maximum area, the rectangle should be a square. Thus, each side = 40/4 = 10 cm.

For maximum area, the rectangle should be a square. Thus, each side = 40/4 = 10.

For a fixed perimeter, the area is maximized when the rectangle is a square. Thus, side = 10 units.

Power (P) is given by P = V^2/R = (20V)^2 / 10Ω = 400/10 = 40W.

Power (P) is given by P = V^2/R = (20V)^2 / 10Ω = 400/10 = 40W.

Rotational kinetic energy K.E. = (1/2)Iω².

L = Iω, if I is halved and ω is doubled, L' = (1/2)(2ω) = L.

Time period (T) = Total time / Number of oscillations = 40 s / 20 = 2 s.

The time period T of a simple pendulum is given by T = 2π√(L/g). For L = 1 m and g = 9.8 m/s², T = 2π√(1/9.8) ≈ 2.0 s.

The period T of a simple pendulum is given by T = 2π√(L/g). Rearranging gives L = (T^2 * g) / (4π^2). Using g = 9.8 m/s² and T = 2 s, we find L = (2^2 * 9.8) / (4π^2) ≈ 1 m.

The strength of the magnetic field in a solenoid is primarily determined by the number of turns per unit length and the current flowing through it.