To determine the density of a solid sphere, its mass is measured as 10.00 g using an instrument with a least count of 0.01 g . Its diameter is measured as 2.00 mm using a screw gauge having a pitch of 1 mm and 100 divisions on its circular scale. The maximum percentage error in the calculated density of the sphere is

Step-by-step solution

The least count of the screw gauge is given by: Least count = Pitch Number of circular scale divisions = 1 mm 100 = 0.01 mm This least count represents the absolute error in the measurement of the diameter, so D = 0.01 mm . The absolute error in mass is the least count of the weighing instrument, so m = 0.01 g . The density of a sphere is given by: = m V = m 4 3 ( D 2 )^3 = 6m D^3 The maximum relative error in density is: = m m + 3 D D Percentage error in mass m is: m m 100 = 0.01 10.00 100 = 0.1 % Percentage error