Question

Find the dimensions of a/b in the relation P= a-x^2/bt, where x is distance, t is time and P is pressure.
please help me...​

Answer 1

Answers: answer in the above photo

Answer 2

we have to find the dimensions of a/b in the relation P = $\frac{a-x^2}{bt}$  , where x is distance , t is time and P is pressure.

solution : dimentions of a = dimensions of x² = [L]² = [L²]

now dimensions of P = dimensions of $\frac{a-x^2}{bt}$ = $\frac{\text{dimensions of a}}{\text{dimensions of bt}}$

⇒ [ML⁻¹T⁻²] = $\frac{[L^2]}{b[T]}$

⇒ b = $\frac{[L^2]}{[T][ML^{-1}T^{-2}]}$ = [M⁻¹L³T]

∴ the dimensions of a/b = [L²]/[M⁻¹L³T] = [ML⁻¹T⁻¹]

therefore the dimensions of a/b is [ML⁻¹T⁻¹]