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:
Pressure has dimensions [ML⁻¹T⁻²]. Energy per unit volume: Energy is [ML²T⁻²], volume is [L³], so [ML²T⁻²]/[L³] = [ML⁻¹T⁻²], matching pressure. Force per unit length is [MLT⁻²]/[L] = [MT⁻²]. Momentum per unit area is [MLT⁻¹]/[L²] = [ML⁻¹T⁻¹]. Power per unit volume is [ML²T⁻³]/[L³] = [ML⁻¹T⁻³]. This dimensional equivalence explains why pressure appears in Bernoulli's equation alongside energy density. Memory aid: Pressure and energy density both represent stored energy per spatial dimension.
No comments yet. Be the first to start the discussion!