In an experimental set up, the density of a small sphere is to be determined. The diameter of the small sphere is measured with the help of a screw gauge, whose pitch is $$0.5$$ mm and there are $$50$$ divisions on the circular scale. The reading on the main scale is $$2.5$$ mm and that on the circular scale is $$20$$ divisions. If the measured mass of the sphere has a relative error of $$2$$%, the relative percentage error in the density is

Question

Infinity Learn · Accepted Answer

$$=PitchTotal$$  divisions  on  circular  scale∴  Least $$count=0.550=0.01$$  $$mm=$$ΔrDiameter $$=$$ Main scale $$+$$ Circular scale × Least $$count=2.5+20$$×$$0.550=2.70$$  mm∵Δ$$rr=0.012.70$$Δrr×$$100=12.7Density$$, $$D=mV=m43$$π$$(r2)3Here$$, r is diameter∴ΔDD×$$100={$$Δ$$mm+3($$Δ$$rr)}$$×$$100=$$Δmm×$$100+3$$×Δrr×$$100=2$$%$$+3$$×$$12.7=3.11$$%

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material