Question

The side of a cube is measured by Vernier callipers($10$ divisions of a Vernier scale coincide with $9$ divisions of main scale, where $1$ division of main scale is $1$mm). The main scale reads $10$mm and first division of Vernier scale coincides with the main scale. Mass of the cube is $2.736$g. Find the density of the cube in appropriate significant figures.

• A. Density $=3.66g/c{m}^3$.
• B. Density $=2.66g/c{m}^3$.
• C. Density $=4.66g/c{m}^3$.
• D. Density $=6.66g/c{m}^3$.

Answer 1

The correct option is B Density $=2.66g/c{m}^3$.

$\begin{array}{cc}10VSD& =9MSD\\ 1VSD& =0.9MSD\\ 1MSD& =1mm\\ 1VSD& =0.9\times 1\\ & =0.9mm\end{array}$

$\begin{array}{cc}MSR& =10mm\\ VSR& =1\times L\cdot C\\ L\cdot C\cdot & =\mathrm{1\; MSD}-1VSD\\ & =1-0.9\\ & =0.1mm\end{array}$

$\begin{array}{c}\text{VSR}=0.1mm\\ \text{final reading}\text{(side of the}\text{cube a)}=10+0.1\\ \begin{array}{cc}\text{Volume}& =a^3\\ & =(10.1{)}^3\\ & =1030.301{mm}^3\\ \text{Mass}=2.736g& \end{array}\end{array}$

$\text{Density}=\frac{2.736}{1030.301\times {10}^{-3}}=2.66gm/{cm}^3$