Question

The least count of a stopwatch is $\frac{1}{5}sec$. The time of $20$ oscillations of a pendulum is measured to be $25sec$. The minimum percentage error in the measurement of time will be:

Answer 1

Step 1: Given Data

The least count of the stopwatch is, $∆x=\frac{1}{5}sec=0.2s$

The number of oscillations for which the time measured is, $x=20$

The measured time is, $t=25sec$

Step 2: Formula used

Error % = $\frac{∆x}{x}\times 100$

Step 3: Calculation

The time period of each oscillation = Given time/ number of oscillations

$\Rightarrow T=\frac{t}{x}=\frac{25}{20}=1.25s$

Error in the time period per each oscillation = least count/number of oscillations

$∆T=\frac{∆x}{x}=\frac{0.2}{20}$

⇒ error % = $\frac{∆T}{T}\times 100$

⇒ error % = $\frac{{\displaystyle \left(\frac{0.2}{20}\right)}}{1.25}\times 100$

⇒ error % = $0.8\%$

⇒ The minimum percentage error in the given measurement is $0.8\%$