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Q.

A student measures the time period of 100 oscillations of a simple pendulum four times. The data set is 90 s, 91 s, 95 s. and 92 s. If the minimum division in the measuring clock is 1 s, then the reported mean time should be

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a

92 ±2s

b

92 ± 5.0 s

c

92 ± 1.8 s

d

92 ± 3 s

answer is A.

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Detailed Solution

Measured time period of 100 oscillations are 90 s, 91 s, 95 s and 92 s.Mean value of time, tm = 90+91+95+924 = 92 sAbsolute error in measurement|∆t1| = |tm-t1| = 2s|∆t2| = |tm-t2| = 1 s|∆t3| = |tm-t3| = 3s|∆t4| = |tm-t4| = 0 sMean absolute error ∆tmean = 2+1+3+04 = 1.5 sBut the least count of the measuring clock is 1 s.so it cannot measure up to 0.5 second so we have to round it off. So mean error will be 2 secondHence mean time 92 ± 2 s
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