Wavelength λ is given by the formula λ = v/f. Here, v = 340 m/s and f = 440 Hz. Thus, λ = 340/440 = 0.7727 m, approximately 0.77 m.

Time period (T) = 1 / frequency = 1 / 440 Hz ≈ 0.00227 s

Time period T = 1/f = 1/440 Hz ≈ 0.00227 s.

Time period (T) = 1 / frequency = 1 / 440 Hz ≈ 0.00227 s.

The potential difference V = E * d = 200 N/C * 3 m = 600 V.

The torque τ = Mg(L/2) and moment of inertia I = (1/3)ML². Using τ = Iα, we find α = 3g/2L.

Using conservation of energy, potential energy at the top = rotational kinetic energy at the bottom. mgh = (1/2)Iω^2. For a rod, I = (1/3)ML^2, h = L/2. Solving gives ω = √(3g/L).

Using conservation of energy, the potential energy lost equals the rotational kinetic energy gained. The angular velocity ω can be derived as ω = √(2g/L)(1-cosθ).

Using conservation of energy, potential energy at the top converts to rotational kinetic energy at the bottom. The angular speed ω = √(3g/L).

Using conservation of energy, potential energy at the top is converted to rotational kinetic energy at the bottom. The angular velocity ω can be found using the relation ω = √(3g/L).

The moment of inertia of a uniform rod about its center is I = 1/12 ML^2.

Using conservation of energy, potential energy converts to rotational kinetic energy. Angular speed ω = √(3g/L).

Using conservation of energy, potential energy converts to rotational kinetic energy. Angular speed ω = √(3g/L).

The angular acceleration α = τ/I = (MgL/2)/(1/3 ML^2) = 3g/2L.

The moment of inertia of a thin circular ring about an axis through its center is I = MR^2.

For a uniformly charged sphere, the electric field outside the sphere behaves as if all the charge were concentrated at the center, thus E = Q/(4πε₀r²).

If the vaccine is 80% effective, then 20% will still contract the disease. Therefore, expected cases = 20% of 1000 = 200.

Using the formula s = ut + (1/2)at²; s = 0 + (1/2)(2)(10²) = 100 m.

Using the formula s = ut + (1/2)at², where a = (v-u)/t = (36-0)/12 = 3 m/s², we find s = 0 + (1/2)(3)(12²) = 216 m.

Convert speed to m/s: 60 km/h = 16.67 m/s. Deceleration = (final velocity - initial velocity) / time = (0 - 16.67) / 5 = -3.33 m/s², approximately 3 m/s².

Total distance = 100 km + 50 km = 150 km; Total time = 2 h + 1 h = 3 h. Average speed = Total distance / Total time = 150 km / 3 h = 50 km/h.

Average speed = total distance / total time = 100 m / 5 s = 20 m/s.

Distance = speed * time = 60 km/h * 2 h = 120 km.

Absolute error is the same as the uncertainty, which is ±0.1 V.

Maximum possible voltage = Measured value + Uncertainty = 12.0 + 0.2 = 12.2 V.

Fractional error = (absolute error / measured value) = 0.3 / 15.0 = 0.02.

The absolute error is given directly as ±5 V.

Relative error = Absolute error / Measured value = 10 / 1000 = 0.01.

Using the formula for density (density = mass/volume), the uncertainty in density can be calculated using the formula for propagation of uncertainty.

Relative error = (Absolute error / Measured value) * 100 = (5 / 200) * 100 = 2.5%