Wavelength λ = v/f = 1500/(50 × 10³) = 1500/50000 = 0.03 m = 3 cm. Higher frequencies in denser mediums produce shorter wavelengths.

Electric field at surface: E = kQ/r² = (9 × 10⁹ × 8 × 10⁻⁶)/(0.02)² = (72)/(4 × 10⁻⁴) = 1.8 × 10⁷ N/C.

Carnot efficiency: η = 1 - (T_cold/T_hot) = 1 - (300/400) = 1 - 0.75 = 0.25 = 25%. This is the theoretical maximum for any heat engine.

At critical angle θ_c, refracted ray becomes parallel to the interface. Beyond this angle, no refraction occurs; light completely reflects back into the denser medium (total internal reflection). This principle enables fiber optics.

Young's modulus is a material property independent of the wire's dimensions or elastic deformation state. It depends only on the material composition and atomic structure, not on physical changes.

Velocity is a vector quantity with both magnitude and direction, unlike speed which is scalar. Velocity can be negative, and in circular motion, velocity constantly changes direction.

Using v² = u² - 2gh, where final velocity v = 0, u = 20 m/s, g = 10 m/s². Therefore, 0 = 400 - 20h, giving h = 20 m.

Newton's Second Law: F = ma, where acceleration is directly proportional to force and inversely proportional to mass.

Using F = ma, F = 2 × 5 = 10 N. This is a direct application of Newton's Second Law.

Initial KE = ½m(v)² + ½m(2v)² = 2.5mv². Final velocity = 3v/2 (by momentum conservation). Final KE = ½(2m)(3v/2)² = 2.25mv²/4 = 0.84mv². Loss = 2.5 - 0.84 = 1.66, which is 2/3 of initial KE.