The density of a solid ball is to be determined in an experiment. The diameter of the ball is measured with 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 ball has relative error of 2%, the relative percentage error in density is
Aditya Pathak
8 Years agoGrade 12th pass
1 Answer
Arun
Approved Tutor Answer8 Years ago
Dear student
Diameter is = 2.5 + (0.5 * 20/50) = 2.7
Error in diameter estimation = delta r = 0.01 mm
delta D/D = 0.01/2.7 = 0.0037
Now
Density = mass/volume
Take log
log (density) = log (m) + ln (4/3 *pi* r³)
delta (density) / density = 3.1%
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