If X = a²b³/c², and percentage errors in a, b, c are 2% each, the maximum percentage error in X is MCQ with Answer and Explanation

Explanation:
Resonance (amplification at natural frequency) is exploited in musical instruments (e.g., guitar body resonates with string frequencies) and tuning forks (designed to vibrate at precise frequency for calibration). Memory tip: 'Resonance applications: musical instruments (amplify sound), tuning forks (frequency standard), bridges (avoid resonance to prevent collapse)'. This application question tests wave phenomena uses, frequently appearing in competitive exams. Always link physical principles to practical applications; competitive exams emphasize real-world relevance of physics concepts, including both beneficial and hazardous aspects of resonance.

Explanation:
a ∝ -x; magnitude maximum when |x| maximum (extremes). At mean position x=0 ⇒ a=0. Velocity maximum at mean position. Memory aid: 'SHM: a max at extremes, v max at center'. Oscillation concept frequently tested in competitive exams to verify SHM characteristics understanding.

Explanation:
v_esc ∝ √(M/R). New ∝ √(4M/2R) = √(2M/R) = √2 √(M/R) = √2 v.