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

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

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.

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.

Using conservation of energy, potential energy converts to kinetic energy. For a solid cylinder, v = √(2gh).

Using conservation of energy, potential energy at the top = kinetic energy at the bottom. For a solid sphere, v = √(5gh/7). Thus, speed at the bottom is √(3gh).

Using conservation of energy, potential energy at height h = kinetic energy at the bottom. For a solid sphere, v = √(3gh).

Wavelength λ = v/f = 343 m/s / 686 Hz = 0.5 m.

The wavelength λ is given by λ = v/f. Thus, λ = 340/170 = 2 m.

Using h = 0.5 * g * t^2, we have 45 = 0.5 * 10 * t^2. Solving gives t^2 = 9, so t = 3 s.

First convert speed to m/s: 72 km/h = 20 m/s. Deceleration = (final velocity - initial velocity) / time = (0 - 20) / 5 = -4 m/s².