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  • The diameter of the ball is measured with a screw gauge, whose pitch is 1 mm and there are 100 divisions on t

The diameter of the ball is measured with a screw gauge, whose pitch is 1 mm and there are 100 divisions on the circular scale. The density of a solid ball is to be determined in an experiment. The reading on the main scale is 3.5 mm and that on the circular scale is 10 divisions. If the measured mass of the ball has a relative error of 2%, the relative percentage error in the density is

Option: 1

0.9 %


Option: 2

2.4 %


Option: 3

3.1 %


Option: 4

2.83 %


Answers (1)

best_answer

\text {Least count of the screw gauge} =1 / 100=0.01 \mathrm{~mm}\\\\ \text {Diameter of the ball,} \\\\\ D=3.5 \mathrm{~mm}+10 \times 0.01 \mathrm{~mm}=3.5+0.1=3.6 \mathrm{~mm}\\\\\ Density, \rho=\frac{M}{\text { vol }}\\\\ \text {The relative percentage error in density} \\\\ =2 \%+\left(3 \times \frac{0.01}{3.7} \times 100\right)=2.83 \%

So, correct option is D.

Posted by

vishal kumar

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