Question

The side of a cube is measured by vernier caliper ($10$ divisions of vernier scale coincide with $9$ divisions of main scale, where $1$ division of main scale is $1\text{mm}$). The main scale reads $10\text{mm}$ and the first division of the vernier scale coincides with the main scale. The maximum $\%$ error in measurement of volume of the cube will be

• A. $5\%$
• B. $8\%$
• C. $3\%$
• D. $6\%$

Answer 1

The correct option is C $3\%$

Least count of vernier caliper
$LC=\frac{\text{Smallest division on main scale}}{\text{Number of divisions on vernier scale}}$
$\Rightarrow LC=\frac{1}{10}=0.1\text{mm}$
$\therefore \Delta L=0.1\text{mm}$
Side length $\left(L\right)$ of the cube = Scale reading
$=10\text{mm}+(1\times 0.1\text{mm})=10.1\text{mm}$
Volume of cube $\left(V\right)=L^3$
$\Rightarrow \frac{\Delta V}{V}=\frac{3\Delta L}{L}=\frac{3\times 0.1}{10.1}=0.03$
$\Rightarrow \frac{\Delta V}{V}\times 100=0.03\times 100=3\%$
$\%$ error in volume $=3\%$
Hence, option $\left(a\right)$ is the correct answer.