Let x and α stand for distance. Is dimensionally

correct?

Theory of relativity reveals that mass can be converted into

energy. The energy E so obtained is proportional to certain powers of

mass m and the speed c of light. Guess a relation among the

quantities using the method of dimensions.

Let I = current through a conductor, R = its resistance and V =

potential difference across its ends. According to Ohm’s law, product

of two of these quantities equals the third. Obtain Ohm’s law from

dimensional analysis. Dimensional formulae for R and V are ML²I^-2T³

and ML² T^-3 I^-1 respectively.

The frequency of vibration of a string depends on the length L

between the nodes, the tension F in the string and its mass per unit

length m. Guess the expression for its frequency from dimensional

analysis.

Test if the following equations are dimensionally correct:

A. B.

C. D.

where h = height, S = surface tension, ρ = density, P = pressure,

V = volume, η = coefficient of viscosity, v = frequency and I =

moment of inertia.