Question

# A physical quantity $$X$$ is represented by $$X = (M^x L^{-y}T^{-z})$$. The maximum percentage errors in the measurement of $$M, L$$ and $$T$$, respectively, are $$a\%, \ b\%$$ and $$c\%$$. The maximum percentage error in the measurement of $$X$$ will be:

A
(ax+bycz)%
B
(axbycz)%
C
(ax+by+cz)%
D
(axby+cz)%

Solution

## The correct option is C $$(ax + by + cz)\%$$$$X=\left[ { M }^{ x }{ L }^{ -xy }{ T }^{ -z } \right]$$% error in $$M=a$$%% error in $$L=b$$%% error in $$T=c$$%$$\dfrac { \Delta X }{ X } \times 100=\left[ x\dfrac { \Delta M }{ M } +y\dfrac { \Delta L }{ L } +z\dfrac { \Delta T }{ T } \right] \times 100$$                     $$=ax+by+cz$$Maximum error in $$X=\left( ax+by+cz \right)$$%Physics

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