A physical quantity is represented by $X = M^{\alpha}L^{b}T^{- c}.$ If percentage errors in the measurements of $M,L$ and $T$ are $\alpha\%,\beta\%$and $\gamma\%$ respectively, then total, percentage error is

Question

Dr. Abubacker · Accepted Answer

$X = M^{a}L^{b}T^{- c}$ $	herefore\ \ \frac{\mathrm{\Delta}X}{X} = \pm \left\lbrack \alpha\frac{\mathrm{\Delta}M}{M} + b\frac{\mathrm{\Delta}L}{L} + c\frac{\mathrm{\Delta}T}{T} ightbrack$ $= \pm \lbrack a\alpha + \beta b + \gamma cbrack\%$

Q. A physical quantity is represented by $X = M^{\alpha}L^{b}T^{- c}.$ If percentage errors in the measurements of $M,L$ and $T$ are $\alpha\%,\beta\%$and $\gamma\%$ respectively, then total, percentage error is

Explanation

Reviewed by Dr. Abubacker

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