A) \[(\eta \alpha -\theta \beta -\phi \gamma )%\]
B) \[(\theta \beta +\phi \gamma -\eta \alpha )%\]
C) \[\left( \frac{\alpha }{\eta }-\frac{\beta }{\theta }-\frac{\gamma }{\theta } \right)%\]
D) \[(\eta \alpha +\theta \beta +\phi \gamma )%\]
Correct Answer: D
Solution :
Given,\[X=[{{M}^{\eta }}{{L}^{-\theta }}{{T}^{-\phi }}]\] \[\therefore \] \[\frac{\Delta X}{X}\times 100\] \[=\eta \left( \frac{\Delta M}{M}\times 100 \right)+\theta \left( \frac{\Delta L}{L}\times 100 \right)+\phi \left( \frac{\Delta T}{T}\times 100 \right)\]\[\Rightarrow \] \[\frac{\Delta X}{X}\times 100=\eta (\alpha )+\theta (\beta )+\phi (\gamma )\] Thus, maximum percentage error in the measurement of \[X\] is given as \[\frac{\Delta X}{X}\times 100=(\eta \alpha +\theta \beta +\phi \gamma )%\]
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