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 r

Question

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 a relative error of 2% , the relative percentage error in the density is

TestHub · Accepted Answer

Least count of screw gauge = 50 0.5 ​ = 0.01 mm = Δ r Diameter, r = 2.5 mm + 20 × 50 0.5 ​ = 270 mm r Δ r ​ = 2.70 0.01 ​ or r Δ r ​ × 100 = 2.7 1 ​ Now, density d = V m ​ = 3 4 ​ π ( 2 r ​ ) 3 m ​ Here, r is the diameter. ∴ d Δ d ​ = ​ × 100 = { m Δ m ​ + 3 ( r Δ r ​ ) } × 100 m Δ m ​ × 100 + 3 × ( r Δ r ​ ) × 100 ​ ​ = 2% + 3 × 27 1 ​ = 3.11% ​ Analysis of Question (i) Question is moderately difficult. (ii) In practical part, questions in JEE are asked from vernier callipers and screw gauge.

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