A student attempts to derive the relation for the displacement of a vibrating…
PHYSICS · Single correct · CBSE · Physics · Units and Measurements · Units and Measurements
Problem
A student attempts to derive the relation for the displacement of a vibrating particle and expects a result of the form y=Asin(ωt). Why can dimensional analysis alone not predict this functional form?
(a) Because sin(ωt) itself carries the dimensions of length, leading to contradictory dimensions.
(b) Because dimensional analysis can only establish simple proportionality such as y∝Aωt, not a sinusoidal dependence.
(c) Because dimensional analysis cannot determine the mathematical form of a relation that involves a trigonometric function of a dimensionless quantity.
(d) Because trigonometric relationships are valid only when angles are measured in degrees, which dimensional analysis does not take into account.