Maximum velocity in SHM: v_max = ωA = 2πfA = 2π × 2 × 5 = 20π cm/s ≈ 62.8 cm/s.
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.
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.
When a block slides down a frictionless incline, gravity's component along the slope determines the acceleration.
On an incline, gravity acts vertically downward, but only its component parallel to the slope causes acceleration down the incline.
Using F = ma, the net force along the incline equals mass times acceleration. The mass cancels out, giving us a pure kinematic result.
The acceleration down the incline is 4.9 m/s² (Answer: A)
Elastic PE = ½kx² = ½ × 100 × (0.1)² = ½ × 100 × 0.01 = 0.5 J.
Diffraction is the bending of waves around obstacles or through openings. This explains why we can hear sounds around corners.
Using Snell's Law: n₁sinθ₁ = n₂sinθ₂. 1 × sin(30°) = 1.5 × sinθ₂. 0.5 = 1.5sinθ₂. sinθ₂ = 0.333. θ₂ ≈ 19.47°.
Total resistance = 4 + 6 = 10Ω. Using Ohm's law: I = V/R = 10/10 = 1 A.
A tungsten filament's resistance changes significantly with temperature during operation, making it non-ohmic. Metals at constant temperature follow Ohm's law.
