Question

2a) A steel ball bearing is to be manufactured with a diameter of 2 cm. The manufacturing process has a tolerance of £.1 mm in the diameter. Given that the density of steel is about 7.85 cg , estimate the propagated error in the mass of the ball bearing. cm3 , Notel: Use differentials to solve this problem. You must use correct notation. Note 2: mass=volume x density b) Is the error found in part a) significant? Ta get a sense, try computing the percentage error.

Answer 1

las we know that, volume , N=4 ans d radius re 2 mass val f = 7.85 cg/cm3 2cm diagneter the is I Od mm in a error How , ball bearing Therefore, em < d < 21 0.01 2-0.01 cm 1.99 { r £ 2.01 9 cm. 0.995 Ere Lour em3 3) 4.126272<V < 4.257937 32:391235 S M < 33.377705 ego The error in the mass is Į (33.379905- 32-391235) eg. = 0.493235 eg. mass (6) The actual should be , Ma Алт°e Nal, P=7.85 32.882003. of error is, The percentage > 32.et 2003*100) = 105 y. Hence, the error is significant,