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

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

Average velocity = total distance / total time = 400 m / 50 s = 8 m/s.

Average velocity = total displacement / total time. Since the runner returns to the starting point, displacement = 0. Average velocity = 0 m/s.

Gravitational force is inversely proportional to the square of the radius. If radius is tripled, force becomes 1/3² = 1/9.

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.

Magnetic flux (Φ) = B * A = 0.2 T * 0.01 m² = 0.002 Wb. For one turn, the flux is 0.002 Wb.

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

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.

Magnetic field B = μ₀ * (N/L) * I = (4π x 10^-7 Tm/A) * (200/0.5) * 2 = 0.8 T.

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) = Speed (v) / Frequency (f) = 340 m/s / 1700 Hz = 0.2 m.

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

Wavelength (λ) = speed (v) / frequency (f) = 340 m/s / 1700 Hz = 0.2 m.

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

The frequency f can be calculated using the formula v = fλ. Rearranging gives f = v/λ = 340 m/s / 0.85 m ≈ 400 Hz.

Frequency (f) = speed (v) / wavelength (λ) = 340 m/s / 0.85 m ≈ 400 Hz.

Using the wave speed formula v = f * λ, we can rearrange to find λ = v/f. Thus, λ = 343 m/s / 686 Hz = 0.5 m.

Potential Energy in spring (PE) = 0.5 × k × x² = 0.5 × 300 N/m × (0.2 m)² = 0.5 × 300 × 0.04 = 6 J.

Potential Energy (PE) = 0.5 * k * x² = 0.5 * 200 N/m * (0.5 m)² = 25 J.

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

Using h = 0.5 * g * t^2, rearranging gives t = sqrt(2h/g) = sqrt(2 * 45 / 10) = sqrt(9) = 3 s.

Using h = 0.5 * g * t^2, rearranging gives t = sqrt(2h/g) = sqrt(2 * 45 / 10) = sqrt(9) = 3 s.

Using the formula: h = 0.5 * g * t^2. Rearranging gives t = sqrt(2h/g) = sqrt(2 * 45 / 10) = sqrt(9) = 3 s.

Using the formula: h = 0.5 * g * t^2. Rearranging gives t = sqrt(2h/g) = sqrt(2 * 80 / 10) = sqrt(16) = 4 s.

Probability of failing = 1 - Probability of passing = 1 - 0.7 = 0.3.