Question

(F-at)(p-b)=1 find [a/b] where , F is force t is time and p is pressure​

Answer 1

Given :

➳ (F - at) (P - b) = 1

where,

▪ F is force

▪ t is time

▪ P is pressure

To Find :

⟶ Dimension of [a/b].

SoluTion :

✴ Concept : Only like quantities having the same dimensions can be added to or substracted from each other.

✴ Dimension Formula :

$\dag\bf\:Force(F)=[M^1L^1T^{-2}]$

$\dag\sf\:Time(t)=[T^1]$

$\dag\bf\:Pressure(P)=[M^1L^{-1}T^{-2}]$

✴ Dimension of a :

$:\implies\sf\:[F]=[a][t]$

$:\implies\sf\:[M^1L^1T^{-2}]=[a][T^1]$

$:\implies\bf\:[a]=[M^1L^1T^{-3}]$

✴ Dimension of b :

$:\implies\sf\:[P]=[b]$

$:\implies\bf\:[b]=[M^1L^{-1}T^{-2}]$

✴ Dimension of [a/b] :

$:\implies\sf\:\dfrac{[a]}{[b]}=\dfrac{[M^{1}L^{1}T^{-3}]}{[M^1L^{-1}T^{-2}]}$

$:\implies\underline{\boxed{\bf{{\large{[}}\dfrac{a}{b}{\large{]}}=[M^0L^2T^{-1}]}}}$

Answer 2

Answer:

[ba ]=[M 0 L 2 T −1 ] is the answer