Suppose a general physical quantity has the dimensional formula

PHYSICS · Multi-part · CBSE · Physics · Units and Measurements · Units and Measurements

Problem

Suppose a general physical quantity QQ has the dimensional formula [MaLbTc][M^{a}L^{b}T^{c}]. The standard units of mass, length and time are altered so that the new units differ from the old ones by small fractional changes Δm%\Delta m\%, Δℓ%\Delta \ell\% and Δt%\Delta t\% respectively. (i) Show that, to first order in the small percentage changes, the percentage change in the numerical value of QQ is approximately −(a Δm+b Δℓ+c Δt)%-(a\,\Delta m + b\,\Delta \ell + c\,\Delta t)\%. (ii) Using the result of part (i), calculate the percentage change in the numerical value of the coefficient of viscosity, whose dimensional formula is [M1L−1T−1][M^1L^{-1}T^{-1}], when the unit of length is decreased by 5%5\%, the unit of time is increased by 4%4\%, and the unit of mass is unchanged. (iii) Comment briefly on how the change in the unit of viscosity would affect readings in an experiment designed to verify Stokes' law under the new set of units.

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