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` and `m_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.