A Poisson's ratio of 0.5 indicates that the material is incompressible.

Absolute error = Relative error * Measured value = 0.03 * 15.5 m = 0.465 m.

True value is taken as the average of the measured value and the error, which is (30 + 29.9) / 2 = 30.05 m.

Total uncertainty = 3 * 0.5 = 1.5 units.

Relative error = (absolute error / measured value) = 0.1 / 12.3 = 0.0081.

Relative error = (absolute error / measured value) = 0.1 / 5.0 = 0.02 or 2%.

Using conservation of energy: m1*c1*(T1-Tf) = m2*c2*(Tf-T2). Solving gives Tf = 50°C.

Work done = Power × Time = 1500 W × (10 × 60 s) = 90000 J.

The electric field E between the plates of a parallel plate capacitor is given by E = V/d, where d is the separation between the plates.

Maximum speed (v_max) = ωA. Thus, ω = v_max/A = 4/2 = 2 rad/s.

The tangential speed v is given by v = rω.

The tangential speed v is given by v = rω.

Centripetal acceleration a_c = v²/R.

L = mvr = 4 kg * 3 m/s * 2 m = 24 kg·m²/s.

Angular momentum L = mvr, if v is doubled, L also doubles.

The angular momentum is constant because the particle's velocity and distance from the point are constant.

Angular momentum L = mvr, where v is the linear speed and r is the radius of the circular path.

Angular momentum L = mvr, where r is the perpendicular distance from the line of motion to point O.

Using the equation v = u + at, where u = 3 m/s, a = 2 m/s², and t = 5 s, we get v = 3 + (2 * 5) = 3 + 10 = 13 m/s.

Angular velocity ω = v/r = 6 m/s / 3 m = 2 rad/s.

Centripetal acceleration (a_c) = v²/r = (5²)/10 = 2.5 m/s².

Circumference = 2πr = 20π m. Period T = distance/speed = 20π m / 5 m/s = 4π s.

Period T = (2πr)/v = (2π * 10)/5 = 4π s.

Period T = (2πr)/v = (2π * 10)/5 = 4π s.

Time period T = 2πr/v = 2π(10 m) / (5 m/s) = 4π s.

Centripetal acceleration (a_c) = v²/r = (10 m/s)² / (5 m) = 20 m/s².

Angular displacement θ = 0.5αt² for constant angular acceleration.

The time period T = 2π/ω for uniform circular motion.

Centripetal acceleration a_c = v^2/R.

Centripetal force F = mv^2/r.