Question

A dimension is a physical nature of a quantity.

(i) give two (2) limitations of dimensional analysis..
(ii) if velocity (v), time (T) and force (F) were chosen as basic quantities, find the dimensions of mass?​

Answer 1

i) A dimension is the physical nature of a quantity. The two limitations of dimensional analysis is as following:

• Dimesnional analysis is unable to derive relation when a physical quantity depends on more than three factors with dimensions.
• It is unable to derive a formula that contain exponential function, trigonometric function, and logarithmic function.

ii) Given:

Velocity = v

Time = t

Force = F

Force = mass x acceleration

= mass x velocity/time

So, mass= (force x time) / velocity

[mass] = Ftv^-1

Hence, dimesnion of mass is Ftv^-1.