What are the dimensional units of A and B if a volume, V, is given by the equation V=A*t^3+B/t?

1 Answer
Mar 19, 2016

A is L^3/T^3 and B is L^3*T

Explanation:

Any volume can be expressed as cubic length, L^3

Only adding up cubic lengths on the right will give the result of another cubic length on the left (Note: multiplying terms would not do this).

So, given V=A*T^3+B/T, let

A*T^3=L^3 meaning the first term is a volume (cubic length), and
B/T = L^3 meaning the second term is also a volume.

Finally we just solve for the respective letters, A and B.

A=L^3/T^3
B=L^3*T