The following equation gives a relation between the mass `m_(1)` kept on a surface of area A and the pressure p exerted on this area.
`p=((m_(1)+m_(2))x)/(A)`
What must be the dimensions of the quatities x and `m_(2)`?

Explanation

Since all the terms of a mathematical equation should have the same dimensions.
Therefore, `[P]=[((m_(1)+m_(2))x)/A]" "...(i)`
Only the quantities having same dimensions and nature can be added to each other.
Here `m_(2)` is added to mass `m_(1)`
Hence `[m_(2)]=[m_(1)]=[M]`
Also the quantity obtained by the addition of `m_(1)andm_(2)` would have the same dimensions as that of mass.
`therefore[m_(1)+m_(2)]=[M]`
Now going back to equation (i)
`[P]=([m_(1)+m_(2)][x])/([A])`
`rArr[ML^(-1)T^(-2)]=([M][x])/([L^(2)])`
`rArr[ML^(-1)T^(-2)]=[ML^(-2)][x]`
`rArr([ML^(-1)T^(-2)])/([ML^(-2)])=[x]`
`rArr[x]=[LT^(-2)]`
Hence, the quantity x represents acceleration in this example, it is the acceleration due to gravity g. `(m_(1)+m_(2))g` represents the weight exerted by two masses `m_(1),m_(2)` on the area A.