Calculate the maximum percentage error in the measurement of time for a pendulum. The time taken by the pendulum to complete 20 oscillations is 25 seconds. Also, the least count of the stopwatch is ? second.

Given,

Least count of a stopwatch, Δt = ⅕ = 0.2 s

Time taken to complete 20 oscillations, T = 25s

No.of oscillations, N = 20

Percentage error in measurement of time is given as:

\(frac{Delta T}{T}times 100%\)

The relative error is given as:

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 = \(frac{t}{N}\) \(frac{Delta T}{T}=frac{Delta t}{t}\)

= \(frac{Delta T}{T}times 100%\)

= \(frac{Delta t}{t}times 100%\)

= \(frac{0.2}{25}times 100%\)

= 0.8%