InterviewSolution
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InterviewSolution
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V is the volume of a liquid flowing per second through a capillary tube of length l and radius r, under a pressure difference (p). If the velocity (v), mass (M) and time (T) are taken as the fundamental quantities, then the dimensional formula for `eta` in the relation `V=(pipr^(4))/(8etal)`A. `[Mv^(-1)]`B. `[M^(1)v^(-1)T^(-2)]`C. `[M^(1)v^(1)T^(-2)]`D. `[M^(1)v^(-1)T^(-1)]` |
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Answer» Correct Answer - C `V=(piPr^(4))/(8etal) therefore eta=(piPr^(4))/(8Vl)` `pi` and 8 have no dimensions. Writing the dimensional formulae for all quantities, we get `[eta]=([M^(1)L^(-1)T^(-2)][L^(4)])/([L^(3)T^(-1)][L^(1)])[because V="Volume/sec"]` `[eta]=[M^(1)L^(-1)T^(-1)]` But velocity `v=(L)/(T) therefore L=vT` `therefore [eta]=[M^(1)v^(-1)T^(-1)T^(-1)]=[M^(1)v^(-1)T^(-2)]` |
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