Question 281: Units , Dimensions and Error Analysis

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.

Accepted Answer

1 division of main scale = 1 mm
Number of division in vernier scale = 10
Mass of cube = 2.736 g
Least count of vernier callipers = (1 main scale 
division) $$-$$ (1 vernier scale division)
$$\begin{aligned}
& =1 \mathrm{~mm}-\frac{9}{10} \mathrm{~mm} \
& =1 \mathrm{~mm}-0.9 \mathrm{~mm} \
& =0.1 \mathrm{~mm}
\end{aligned}$$
Length of the cube as measured by vernier 
callipers
$$\begin{aligned}
& =10 \mathrm{~mm}+(1 	imes 0.1 \mathrm{~mm}) \
& =10 \mathrm{~mm}+0.1 \mathrm{~mm} \
& =10.1 \mathrm{~mm} \
& =1.01 \mathrm{~cm}
\end{aligned}$$
density of the material of the cube $$=\frac{	ext { mass }}{	ext { volume }}$$
$$\begin{aligned}
ho & =\frac{2.736 \mathrm{~g}}{(1.01)^{3} \mathrm{~cm}^{3}} \
& =2.66 \mathrm{~g} / \mathrm{cm}^{3} \
ho 	ext { in SI } & =2.66 	imes 10^{3} \mathrm{~kg} / \mathrm{m}^{3} .
\end{aligned}$$

Answer

$$5	imes10^3$$

Answer

$$7	imes10^4$$

Answer

$$2.66	imes10^3$$

Answer

$$3.45	imes10^3$$

Units , Dimensions and Error Analysis

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