An experimenter uses a digital stopwatch to record the duration of 40 complete oscillation… — JAMB UTME

An experimenter uses a digital stopwatch to record the duration of $40$ complete oscillations of a simple pendulum. The stopwatch displays a reading of $50.8\text{ s}$ , but it has a known positive zero error of $+0.8\text{ s}$ . What is the correct period of oscillation of the pendulum?

$1.25\text{ s}$ Answer
B
$1.29\text{ s}$
C
$1.27\text{ s}$
D
$0.80\text{ s}$

Answer

The correct period of oscillation is

1.25\text{ s}

To find the true duration of the oscillations, the positive zero error of

+0.8\text{ s}

must be subtracted from the stopwatch display of

50.8\text{ s}

, giving an actual elapsed time of

50.0\text{ s}

. Dividing this corrected time by the

40

complete oscillations gives

T = 50.0\text{ s} / 40 = 1.25\text{ s}

Step-by-Step Solution

Calculate the true time interval by correcting for the instrument zero error.

t_{\text{actual}} = 50.8\text{ s} - 0.8\text{ s} = 50.0\text{ s}

A positive zero error means the timer reads higher than the true time, so the error value must be subtracted.

Calculate the period of a single oscillation by dividing the total corrected time by the number of oscillations.

T = \frac{t_{\text{actual}}}{N} = \frac{50.0\text{ s}}{40} = 1.25\text{ s}

The period

T

is defined as the time required to complete one full oscillation cycle.

Key Concept

Measurement of Time with Zero Error Correction

Estimated Time:1m 30s

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