A particle performs Simple Harmonic Motion (SHM). If its displacement from the mean position is half of its amplitude, the ratio of its kinetic energy to potential energy is: MCQ with Answer and Explanation

Explanation:
Free fall: h = ½gt² ⇒ t = √(2h/g). Thus t ∝ √h. If h' = 4h, t' = √(4h/g) = 2√(h/g) = 2t. Time doubles when height quadruples. Memory aid: 'Free fall time: t ∝ √h; quadruple height ⇒ double time'. This kinematics proportional reasoning problem is frequently tested in competitive exams. Always derive the proportionality from fundamental equations; avoid assuming linear relationships for non-linear motion.

Explanation:
By Ampere's Circuital Law, for a solid wire carrying uniform current, the magnetic field inside (r < R) is B = (mu_0 * I * r) / (2piR^2), meaning B ∝ r (straight line). Outside the wire (r > R), B = (mu_0 * I) / (2pi*r), meaning B ∝ 1/r (rectangular hyperbola). Thus, it increases linearly then decays.

Explanation:
Total internal reflection (TIR) is exploited in optical fibers for light transmission with minimal loss (core-cladding interface). In diamonds, high refractive index (n≈2.4) gives small critical angle (~24°), so most light undergoes TIR, enhancing brilliance through multiple reflections. Memory aid: 'TIR applications: optical fibers (communication), diamonds (sparkle), prisms (binoculars)'. This application question tests optics uses, frequently appearing in competitive exams. Always link physical principles to technological applications; competitive exams emphasize practical relevance of theoretical concepts.