Question 21: Units , Dimensions and Error Analysis

Question

When both jaws of vernier callipers touch each other, zero mark of the vernier scale is right to zero mark of main scale, $4{ }^{	ext {th }}$ mark on vernier scale coincides with certain mark on the main scale. While measuring the length of a cylinder, observer observes 15 divisions on main scale and $5^{	ext {th }}$ division of vernier scale coincides with a main scale division. Measured length of cylinder is $\_\_\_\_$ mm.
(Least count of Vernier calliper $=0.1 \mathrm{~mm}$ )

Accepted Answer

When jaws touch, the vernier zero is to the right of the main scale zero, which indicates a positive zero error.
Coinciding vernier division (CVD) for error $=4$.
Least Count $(\mathrm{LC})=0.1 \mathrm{~mm}$.
So, zero error $=+(\mathrm{CVD} 	imes \mathrm{LC})=+(4 	imes 0.1)=+0.4 \mathrm{~mm}$
Main scale reading $(\mathrm{MSR})=15$ divisions.
Assuming 1 division $=1 \mathrm{~mm}$, then main scale reading is $\mathrm{MSR}=15 \mathrm{~mm}$
Vernier Scale Reading $(\mathrm{VSR})=($ Coinciding vernier division $) 	imes \mathrm{LC}$.
$$ \mathrm{VSR}=5 	imes 0.1=0.5 \mathrm{~mm} $$
Total Observed Reading $=\mathrm{MSR}+\mathrm{VSR}=15+0.5=15.5 \mathrm{~mm}$
True Length $=$ Observed Reading - Zero Error
True Length $=15.5 \mathrm{~mm}-(+0.4 \mathrm{~mm})$
True Length $=15.1 \mathrm{~mm}$
Hence, the correct option is (D).

Answer

15.5

Answer

15.4

Answer

15.9

Answer

15.1

Units , Dimensions and Error Analysis

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