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:
Explanation:
In SHM, Total Energy (E) = 1/2 k A^2. Potential Energy (U) at displacement x is 1/2 k x^2. Kinetic Energy (K) is E - U = 1/2 k (A^2 - x^2). Given x = A/2. U = 1/2 k (A/2)^2 = 1/2 k (A^2 / 4) = E/4. Since total energy is conserved, K = E - E/4 = 3E/4. The ratio of Kinetic to Potential Energy (K:U) is (3E/4) / (E/4) = 3:1.
Explanation:
Resistance R = ρL/A. Volume constant: A ∝ 1/L. Stretching length to 2L reduces area to A/2. New R' = ρ(2L)/(A/2) = 4ρL/A = 4R = 40 Ω. Resistance proportional to (length)² when volume constant.
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