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Convert 76cm of mercury pressure into N...

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

Text Solution

Verified by Experts

In cgs system 76 cm of mercury
pressure `=76xx13.6xx980"dyne cm"^(-2)`
The dimensional formula of pressure P is `[ML^(-1)T^(-2)]`
`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 )[(T_(1))/(T_(2))]^(a)`
`M_(1)=1g, M_(2)=1g`
`L_(2)=1cm, L_(2)=1m`
`T_(1)=1s, T_(2)=1s`
So `a=1,b=-1, c=-2`.
Then
`P_(2)=76xx13.6xx980[(1g)/(1kg)]^(1)[(1cm)/(1m)]^(-1)[(1s)/(1s)]^(-2)`
`=76xx13.6xx980[(10^(-3)g)/(1kg)]^(1)[(10^(-2)m)/(1m)]^(-1)[(1s)/(1s)]^(-2)`
`=76xx13.6xx980xx[10^(-3)]xx10^(2)`
`P_(2)=1.01xx10^(5)Nm^(-2).`
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