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 quantities x and `m_(2)`?

Explanation

Since all the terms of a mathematical equation should have the same dimensions.
Therefore, `[p]=[((M_(1)+m_(2)))/(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)` and `m_(2)` would have the same dimensions as that of mass.
`therefore` `[m_(1)+m_(2)]=[M]`
Now going back to Eq. (i)
`[p]=([m_(1)+m_(2)][x])/([A])`
`Rightarrow` `[ML^(-1)T^(-2)]=([M][x])/([L^(2)])Rightarrow[ML^(-1)T^(-2)]=[ML^(-2)][x]`
`Rightarrow` `([ML^(-1)T^(-2)])/([ML^(-2)])=[x]Rightarrow[x]=[LT^(-2)]`
Hence,the quantity x represents acceleration. In this example, it is the acceleration dur to gravity, `g.(m_(1)+m_(2))g` represents the weight exerted by two masses `m_(1)`,`m_(2)` on the area A.