Question

A physical quantity X is represented by $X=[{{M}^{\eta }}{{L}^{-\theta }}{{T}^{-\text{o }\\!\\!|\\!\\!\text{ }}}].$ The maximum percentage errors in the measurement of M, L and T, respectively are $\alpha$ and $\gamma$ The maximum percentage error in the measurement of X will be

• 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. $(\eta \alpha +\theta \beta +o|\gamma )$

Answer 1

Answer: (D)

$(\eta \alpha +\theta \beta +o|\gamma )$

Answer 2

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 $\frac{\Delta X}{X}\times 100=(\eta \alpha +\theta \beta +o|\gamma )$