In an experiment to determine the density of a cylindrical metal rod, the mass is measured as 1.00 g using a balance with a least count of 0.01 g . The length is measured as 10.0 cm using a meter scale with a least count of 1 mm . The diameter is measured as 2.00 mm using a screw gauge which has a pitch of 1 mm and 100 divisions on its circular scale. The maximum percentage error in the calculated density of the rod

Step-by-step solution

The absolute error in each measurement is equal to the least count of the respective measuring instrument. For mass M : M = 0.01 g Percentage error in M = 0.01 1.00 100 = 1 % For length L : Least count = 1 mm = 0.1 cm L = 0.1 cm Percentage error in L = 0.1 10.0 100 = 1 % For diameter D : Least count of screw gauge = Pitch Number of circular divisions = 1 mm 100 = 0.01 mm D = 0.01 mm Percentage error in D = 0.01 2.00 100 = 0.5 % The density of a cylinder in terms of its diameter is given by = M ( D 2 )^2 L = 4M D^2