Govt. Exams
Using F = ma: a = F/m = 10/2 = 5 m/s². Using v² = u² + 2as: v² = 0 + 2(5)(5) = 50. v = √50 ≈ 7.07 m/s. Checking options again using work-energy: Work = KE; 10×5 = (1/2)(2)v²; v = 5√2 m/s. The closest correct approach gives v² = 50, so v = 5√2 m/s or approximately 7.07 m/s. Option B matches √50.
The Lyman series involves transitions to n=1 from higher energy levels. Balmer series ends at n=2, Paschen at n=3, and Brackett at n=4.
Acoustic impedance (Z) = ρ × c, where ρ is density and c is sound velocity. SI unit is kg/(m²·s). It's crucial for understanding sound reflection and transmission.
Energy of photon: E = hf = 6.63 × 10⁻³⁴ × 5 × 10¹⁴ = 3.315 × 10⁻¹⁹ J ≈ 2.07 eV. KE_max = E - φ = 2.07 - 2 = 0.07 eV. (Recalculation shows approximately 2.08 eV with more precision.)
From orbital mechanics: v = √(GM/r). If r becomes 2r, then v_new = √(GM/2r) = v/√2. Velocity decreases by factor √2.
Due to refraction at the water-air interface, light bends as it exits water. This causes objects to appear at different positions and moving at different speeds than they actually are—an optical illusion, not actual motion change.
Period T = 2π√(m/k) = 2π√(5/200) = 2π√(1/40) = 2π × (1/(2√10)) = π/√10 ≈ π s (approximately).
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.
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.
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.