InterviewSolution
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InterviewSolution
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A sperical body of mass `m` and radius `r` is allowed to fall in a medium of viscosity `eta`. The time in which the velocity of the body increases from zero to `0.63 ` times the terminal velocity `(v)` is called constant `(tau)`. Dimensionally , `tau` can be represented byA. `(mr^(2))/( 6 pi eta)`B. `sqrt((6 pi m r eta)/( g^(2)))`C. ` (m)/( 6 pi eta r v)`D. None of these |
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Answer» Correct Answer - D `[ ( m r^(2))/( 6 pi eta)] = [ (ML^(2))/( ML^(-1) T^(-1))] = [L^(3) T]` As we have `[ eta] = [ML^(-1) T^(-1)]` `[(( 6 pi m r eta)/( g^(2)))^(1//2) ] = [ (( MLML^(-1) T^(-1))/( L^(2) T^(-4)))^(1//2)]` ` [ (m) /( 6 pi eta r v)] = [ (M) /( ML^(-1) T^(-1) LLT^(-1))] = [L^(-1) T^(2)]` Thus , none of the given expressions have the dimensions of time . |
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