Question

Physical quantities are generally not purely numerical: They have a particular dimension or combination of dimensions associated with them. Thus, your height is not 74, but rather 74 inches, often expressed as 6 feet 2 inches. Although feet and inches are different units they have the same dimension--length.

Required:
a. Find the dimensions [V] of volume.
b. Find the dimensions [v] of speed.

Answer 1

a, The dimension of volume is L³

b. The dimension of speed = L/T

Step-by-step explanation:

The three fundamental quantities are Mass, Length and time. Other physical quantities are obtained from or derived from these three. These other quantities are known as derived quantities. The units of the fundamental quantities are Kilogram (kg) for Mass, meters for length, and second for time.

In the given question:

a. Volume = length * breadth * height

since breadth and height all measure length, the dimension of volume becomes:

volume = length * length * length = L³

Thus, the dimension of volume is L³

b. Speed, v = distance/time

Distance measures length, therefore, the dimension of speed will be:

Speed = length / time = L/T

Therefore, the dimension of speed = L/T