A ticker-tape timer connected to a 50\text{ Hz} alternating current mains supply is used t… — JAMB UTME

A ticker-tape timer connected to a $50\text{ Hz}$ alternating current mains supply is used to measure the time interval of a laboratory cart moving down an inclined plane. On the printed tape, $10$ distinct tick spaces are recorded between the initial and final position. A electronic stopwatch running concurrently has a positive zero error of $+0.04\text{ s}$ . What is the true elapsed time interval represented by the ticker tape after properly correcting for the stopwatch zero error?

$0.16\text{ s}$ Answer
B
$0.24\text{ s}$
C
$0.20\text{ s}$
D
$0.22\text{ s}$

Answer

The true elapsed time interval is

0.16\text{ s}

The ticker-tape frequency of

50\text{ Hz}

gives a time interval of

0.02\text{ s}

per space. Ten tick spaces correspond to an uncorrected time of

0.20\text{ s}

. To correct for a positive zero error of

+0.04\text{ s}

, the zero error must be subtracted from the uncorrected reading, yielding a true elapsed time of

0.16\text{ s}

Step-by-Step Solution

Calculate the period of a single tick interval

T = \frac{1}{f} = \frac{1}{50\text{ Hz}} = 0.02\text{ s}

Frequency

f

is the inverse of period

T

for a ticker-tape timer.

Determine the uncorrected total elapsed time from tick spaces

t_{\text{uncorrected}} = 10 \times 0.02\text{ s} = 0.20\text{ s}

Elapsed time equals the number of tick spaces multiplied by the period of one space.

Apply the zero error correction

t_{\text{true}} = t_{\text{uncorrected}} - \text{zero error} = 0.20\text{ s} - 0.04\text{ s} = 0.16\text{ s}

True Reading = Observed Reading - (Zero Error).

Key Concept

Measurement of time using ticker-tape timers and instrument zero error correction

Estimated Time:1m 30s

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