The density of a solid sphere is determined by measuring its mass and radius. The mass is measured using a balance with a least count of 1 g and is found to be 100 g . The radius is measured using vernier calipers and is found to be 2.00 cm . If the maximum percentage error in the calculated density is 2.5 % , the least count of the vernier calipers used to measure the radius is:

Step-by-step solution

The density of a solid sphere is given by the formula: = M V = M 4 3 R^3 The maximum percentage error in the density is given by: 100 = M M 100 + 3 R R 100 Given values: 100 = 2.5 % M = 100 g M = 1 g (least count of the balance) R = 2.00 cm R is the least count of the vernier calipers. Substituting the given values into the error equation: 2.5 = ( 1 100 ) 100 + 3 ( R 2.00 ) 100 2.5 = 1 + 150 R 1.5 = 150 R R = 1.5 150 = 0.01 cm Answer: 0.01 cm