Question
If all the terms in an equation have same dimensions, is it necessary that they have same units? Explain your answer by giving one example.
Solution
For quantities having same dimensions, it is not necessary that they should have the same units.
For example, in the equation W = T
where, W is work,
T is torque,
m is mass, and
v is velocity.
Dimensional formula of each term in the equation is [M1L2T–2 ] but the unit of work is Joule and that of torque is Newton-meter. That is, the units are different.
