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