Convert 76 cm of mercury pressure into `"Nm"^(-2)` using the method of dimensions.

Explanation

In cgs system 76 cm of mercury pressure = `76 xx 13.6 xx 980` dyne `"cm"^(-2)`
The dimensional formula of pressure P is `[ML^(-1)T^(-2)]` , so `P_(1) [M_(1)^(a)L_(1)^(b)T_(1)^(c)] = P_(2)[M_(2)^(a)L_(2)^(b)T_(2)^(c)]`
We have `P_(2) = P_(1) [(M_(1))/(M_(2))]^(a) [(L_(1))/(L_(2))]^(b) [(L_(1))/(L_(2))]^(c)`
`M_(1) = 1 g, M_(2) = 1kg`
`L_(1) = 1 cm, L_(2) = 1m`
`T_(1) = 1 s, T_(2) = 1s`
So, `a = 1, b = -1 and c = -2`
Then, `P_(2 ) = 76 xx 13.6 xx 980`
`[(1g)/(1kg)]^(1) [(1 cm)/(1 m)]^(-1) [(1s)/(1s)]^(-1) = 76 xx 13.6 xx 980 [(10^(-3)kg)/(1 kg)]^(1) [(10^(-2)m)/(1m)]^(-1) [(1s)/(1s)]^(-2)`
`=76 xx 13.6 xx 980 xx [10^(-3)] xx 10^(2)`
`P_(2) = 1.01 xx 10^(5) Nm^(-2)`