Question

39. A boy measures the diameter of a small metal ball using a vernier callipers. He takes the following five read-
ings. 2.48 cm, 2.49 cm, 2.51 cm, 2.50 cm, 2.51 cm
Find its radius with the appropriate % error.
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Answer 1

mean of given observations = (2.48 + 2.49 + 2.51 + 2.50 + 2.51)/5

= 2.498 cm ≈ 2.50 cm

so, radius of the metal ball = 2.50/2 = 1.25cm

now, separately finding absolute error of all observations,

|∆D1| = |2.48 - 2.50| = 0.02

|∆D2| = |2.49 - 2.50| = 0.01

|∆D3| = |2.51 - 2.50| = 0.01

|∆D4| = |2.50 - 2.50| = 0.00

|∆D5| = |2.51 - 2.50| = 0.01

so, sum of absolute errors = 0.02+ 0.01 + 0.01 + 0.01 = 0.05

mean absolute error = 0.05/5 = 0.01

now, fractional error = mean absolute error/mean

= 0.01/2.50 = 1/25 = 0.04

so, percentage error = 100× 0.04 = 4%

hence, the radius is 1.25 with percentage error 4%

Answer 2

Answer:

Please refer to the attachment.

Hope this helped!

@Shailene