Question 308: 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

The distance moved on the linear scale when circular scale makes one complete rotation is p = 1 mm (pitch). The number of divisions on the circular scale is N = 100. Thus, one division on the circular scale is LC = $${p \over N} = {1 \over {100}}$$ = 0.01 mm. The linear scale reading (LSR) is 1 mm and the circular scale reading (CSR) is 47. Thus, the diameter of the wire is
d = LSR + CSR $$	imes$$ LC
= 1 + 47 $$	imes$$ 0.01 = 1.47 mm = 0.147 cm.
The curved surface area is S = 2$$\pi$$rL. That is,
$$S = 2\pi \left( {{d \over 2}} ight)L$$
$$S = \pi dL = \pi \left( {{{1.47} \over {10}}} ight)5.6 = $$ 2.5848 cm
2
= 2.6 cm
2
which is corrected to two significant digits.

Units , Dimensions and Error Analysis

Integer / Numeric Answer Type