Question

A vernier least count $0.1mm$ percentage error in volume of cube of side $30mm$

• A. $0.3\%$
• B. $1\%$
• C. $3\%$
• D. $0\%$

Answer 1

The correct option is B $1\%$

$\begin{array}{c}\mathrm{side}\left(a\right)=30mm\\ \text{Volume}\left(v\right)=a^3\end{array}$

$\begin{array}{c}\text{Taking log both side and differentiating}\\ \begin{array}{cc}\frac{\delta V}{v}=& \frac{3\delta a}{a}\\ \delta a=0.1mm\text{(given)}& \\ \frac{\delta V}{V}\times 100\%& =3\times \frac{0.11}{388}\times 1008\\ & =\frac{3}{3}\times 1\\ & =1\%.\end{array}\end{array}$