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Solution

Q.
Time intervals measured by a clock give the following readings: 1.25 s, 1.24 s, 1.27 s, 1.21 s and 1.28 s

What is the percentage relative error of the observations

1 1.6%

2 2%

3 4%

4 16%

Ans.
a) $\bar{t} = \frac{1.25 + 1.24 + 1.27 + 1.21 + 1.28}{5}$

$= 1.25 S$

${(∆ t)}_{1} = 1.25 - 1.25 = 0$

${(∆ t)}_{2} = 1.24 - 1.25 = - 0.01$

${(∆ t)}_{3} = 1.27 - 1.25 = 0.02$

${(∆ t)}_{4} = 1.21 - 1.25 = - 0.04$

${(∆ t)}_{5} = 1.28 - 1.25 = 0.03$

$| ∆ \bar{t} | = \frac{| {(∆ t)}_{1} | + | {(∆ t)}_{2} | + | {(∆ t)}_{3} | + | {(∆ t)}_{4} | + | {(∆ t)}_{5} |}{5}$

$= \frac{0 + 0.01 + 0.02 + 0.04 + 0.03}{5} = 0.02$

$\frac{| ∆ \bar{t} |}{\bar{t}} \times 100 = \frac{0.02}{1.25} \times 100 = 1.6 %$

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