Which of the following electromagnetic waves has the highest frequency? MCQ with Answer and Explanation

Explanation:
The number of half-lives (n) that have passed is total time / half-life = 15 / 5 = 3 half-lives. The fraction of the sample remaining undecayed is given strictly by the formula (1/2)^n. Therefore, the fraction remaining is (1/2)^3 = 1/2 * 1/2 * 1/2 = 1/8.

Explanation:
For spring-mass system undergoing SHM, time period T = 2π√(M/k), derived from F = -kx = Ma ⇒ a = -(k/M)x, so ω² = k/M, T=2π/ω=2π√(M/k). Option B has inverse ratio; C misses factor 2; D is for pendulum. Memory tip: 'Spring: T ∝ √(M/k); Pendulum: T ∝ √(l/g)'. This standard formula is frequently tested in oscillations sections of competitive exams. Always verify dimensions: √(kg / (N/m)) = √(kg·m/N) = √(s²) = s, correct for time period.

Explanation:
A transformer core is subject to alternating magnetic fields, tracing out a hysteresis loop repeatedly. To minimize energy loss (hysteresis loss), the area of this loop must be small, requiring low coercivity (easily demagnetized). It also requires low retentivity so it loses magnetism rapidly when current stops. Steel, conversely, has high retentivity and coercivity, used for permanent magnets.