A quantity is suspected to depend on acceleration due to gravity
PHYSICS · Single correct · CBSE · Physics · Units and Measurements · Units and Measurements
Problem
A quantity Q is suspected to depend on acceleration due to gravity g, density ρ, viscosity η and a characteristic length r. Why may dimensional analysis fail to give a unique formula for Q in this case?
(a) Because viscosity is a derived quantity, dimensional analysis cannot be applied to it, leading to ambiguity.
(b) Because the number of variables exceeds the number of fundamental dimensions, leading to more unknown exponents than independent equations.
(c) Because the suspected dependence may contain an undetermined dimensionless constant, which dimensional analysis alone cannot fix.
(d) Because the variables involve four different fundamental dimensions, making the dimensional equations over-determined and hence unsolvable uniquely.