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Difficulty: MediumMeasurement of Time

A ticker-tape timer connected to an alternating current supply operates at a frequency of 50 Hz50\text{ Hz}. If a tape pulled through the timer displays 66 consecutive dots, what is the total time interval represented by this section of tape?

  1. 0.10 s0.10\text{ s}Answer
  2. B
    0.12 s0.12\text{ s}
  3. C
    0.02 s0.02\text{ s}
  4. D
    0.25 s0.25\text{ s}

Answer

The total time interval represented by the section of tape is 0.10 s0.10\text{ s}.
The frequency of 50 Hz50\text{ Hz} means each tick interval takes T=150=0.02 sT = \frac{1}{50} = 0.02\text{ s}. For 66 consecutive dots, there are 55 intervals between them. The total time elapsed is 5×0.02 s=0.10 s5 \times 0.02\text{ s} = 0.10\text{ s}.

Step-by-Step Solution

1
Calculate the period TT of a single tick interval
T=1f=150 Hz=0.02 sT = \frac{1}{f} = \frac{1}{50\text{ Hz}} = 0.02\text{ s}
The period of oscillation of the timer represents the time elapsed between two successive dots.
2
Determine the number of time intervals (spaces) between 6 consecutive dots
Number of intervals = 6−1=5 intervals6 - 1 = 5\text{ intervals}
Time measurement on a ticker tape is based on the number of spaces between dots, not the count of dots themselves.
3
Calculate the total time interval tt
t=5×0.02 s=0.10 st = 5 \times 0.02\text{ s} = 0.10\text{ s}
Multiply the number of spaces by the time period per space.

Key Concept

Measurement of time using a ticker-tape timer
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Topics

Measurement of Time

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