Distance = speed * time = 10 m/s * 5 s = 50 m.

For rolling without slipping, a_cm = (2/3)g sin(θ).

Rotational kinetic energy K.E. = (1/2)Iω². For a disc, I = (1/2)MR², thus K.E. = (1/4)MR²ω².

From Newton's second law for rotation, τ = Iα, thus α = τ/I.

Using F = ma, mass m = F/a = 10 N / 2 m/s² = 5 kg.

Work done = Force × Distance = 10 N × 5 m = 50 J

Work done = Force × Distance = 10 N × 5 m = 50 J

Work done = Force × Distance = 10 N × 5 m = 50 J.

Using F = ma, we find a = F/m = 30 N / 6 kg = 5 m/s².

Work = Force * Distance = 50 N * 4 m = 200 J.

Work done by the gas during expansion at constant pressure is W = PΔV. Here, ΔV = 5 L - 2 L = 3 L, so W = 1 atm * 3 L = 3 L·atm.

In an isothermal process, the work done by the gas is equal to the heat absorbed. Therefore, work done = 600 J.

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.

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.