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