Q.7
In an experiment, the time t for a ball to fall from rest through a vertical distance h was measured. The given graph was plotted by a student who knew the equation h = ½ gt2 applies.
Which statement is an explanation for the intercept?
A Air resistance should be taken into account for larger values of h.
B There is a constant delay between starting the timer and releasing the ball.
C There is an error in the timer which consistently makes it run fast.
D The student should have plotted h against t2.
Answer: B
The graph shows a relationship of
√h = kt – c
Where k, c = positive constants.
Only B, a constant delay between starting the timer and releasing the ball will produce a t-intercept (h = 0) at t > 0.
Q.8
Which one the following techniques could reduce or eliminate the systematic error of the quantity being measured?
A adjusting an ammeter to remove its zero error before measuring a current
B measuring several internodal distances on a standing wave to find the meas internodal distance
C measuring the diameter of a wire repeatedly and calculating the average
D timing a large number of oscillations to find a period
Answer: A
Systematic errors cannot be reduced by repeated readings, measuring multiple measurands together, or measuring a large measurand.
Q.9
Four balances were used to measured the mass of a 1.000 kg weight. The reading was taken five times at each balance.
The values obtained and the means are shown in the given table.
Which balance is not very precise but has the smallest systematic error?
Answer: B
Balance B has the smallest systematic error, i.e. its mean is closest to the true value, but is not very precise, i.e. readings are scattered widely about their mean.
Q.10
In an experiment to measure the acceleration of free fall g, each of four students made a series of measurements. The results are as shown in the given table.
Which of the students obtained results that could be considered precise but not accurate?
Answer: D
Precise ≡ small spread in measurements
accurate ≡ close to true value (9.81)
Student D’s results have the smallest spread but the mean og his measurements is the furthest from the true value.
Q.11
A steel rule, reading to ±1 mm, gives the following results when used to measure the length of a bar.
892 mm, 891 mm, 892 mm, 891 mm, 891 mm, 892 mm
It the true length of the bar is 895 mm, which row in the table is correct?
Answer: B
Averate readings = 891.5 is 3.5 mm less that true value of 895 mm and so results are not accurate to within 1 mm, is within ±0.5 mm of all readings and so results are precise to within 1 mm.
Q.12
Systematic and random errors may be compared by contrasting the following pairs of properties:
P1 : error can possibly be eliminated
P2 : error cannot possibly be eliminated
Q1 : error is of constant sign and magnitude
Q2 : error is of varying sign and magnitude
R1 : error will be reduced by averaging repeated measurements
R2 : error will not be reduced by averaging repeated measurements
What are the properties applicable to random errors?
A P1, Q2, R2 B P1, Q2
Answer: C
Random errors refer to the scatter of readings about a mean value (usually the sum of the true value and all systematic errors). The errors are of varying sign magnitude and cannot be eliminated, but could be reduced by taking the average of repeated readings.
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