The side of a cube is measured by Vernier callipers ( $10$ divisions of the vernier scale coincide with $9$ divisions of the 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. The mass of the cube is $2.736 g$ . Find the density of cube in appropriate significant figures.

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Solution

Least count of Vernier callipers
= $\frac{1 d i v i s i o n o f m a i n s c a l e}{N u m b e r o f d i v i s i o n s i n V e r n i e r s c a l e} = \frac{1}{10} = 0.1 m m$
Side of cube = $10 m m + 1 \times 0.1 m m = 1.01 c m$
Now, density = $\frac{M a s s}{V o l u m e} = \frac{2.736 g}{(1.01)^{3} c m^{3}} = 2.66 g c m^{- 3}$

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