Question

Write the dimensions of a and b in the relation, $P=\frac{b-x^2}{at}$ where P is power, x is distance and t is time.

Answer 1

Given $P=\frac{b-x^2}{at}$
$\Rightarrow Pat=b-x^2$
Implies both b and x^2 should have same units.
We know that $\left[x^2\right]=L^2$
Hence, $\left[b\right]=L^2$
Similarly, $\left[Pat\right]=\left[x^2\right]=L^2$
$\left[a\right]=\frac{L^2}{\left[Pt\right]}=\frac{L^2}{\left(M{L}^2{T}^{-3}\right)\left(T\right)}=M^{-1}{L}^0{T}^2$