Single Choice

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$$(ax + by - cz)\%$$
B$$(ax - by - cz)\%$$
C$$(ax + by + cz)\%$$
Correct Answer
D$$(ax - by + cz)\%$$

Solution

$$X=\left[ { M }^{ x }{ L }^{ -xy }{ T }^{ -z } \right] $$
% 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 $$X=\left( ax+by+cz \right) $$%

SIMILAR QUESTIONS

Measurement and Errors

The errors which are estimated by statistical methods are:

Measurement and Errors

In a meter bridge experiment, we try to obtain the null point at the middle. This reduces :

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