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

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 = 0 .5 50 = 0 .01 mm Diameter of ball D = 2.5 mm + 20 0 .01 D = 2.7 mm ρ = M v o l = M 4 3 π D 2 3 ∆ ρ ρ m a x = ∆ M M + 3 ∆ D D ; ∆ ρ ρ m a x = 2 % + 3 0.01 2.7 × 100 % ∆ ρ ρ = 3.1 %

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