The least count of a stop watch is 1 5

Asked by admin @ 02/08/2021 in Physics viewed by 251 People

The least count of a stop watch is 1/5 second the time of 20 oscillation of a pendulum is measured to be 25 seconds the maximum percentage error in the meaaurment of time

Answered by admin @ 02/08/2021

Final. Answer :Maximum percentage error in time taken., = 0.8%

Steps :

1) Least count ,

$\Delta t =\frac{1}{5}=0.2s$

Time taken to complete 20 oscillations, T = 25 s

No. of Oscillations , N = 20

Percentage error in measurement of time ,

$\frac{\Delta T}{T}*100\% =?$

We shall find relative error,

$T = \frac{t}{N}\\ \\=> ln(T) = ln(\frac{t}{N})\\ \\=> ln(T) = ln(t)-ln(N) \\ \\=>\frac{\Delta T}{T}=\frac{\Delta t}{t}+0$

We get ,

$T=\frac{t}{N}\\ \\=\frac{\Delta T}{T}=\frac{\Delta t}{t}\\ \\=\frac{\Delta T}{T}*100 \%\\ \\ =\frac{\Delta t}{t}*100 \%\\ \\ = \frac{0.2}{25}*100 = 0.8\%$

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