| a. |
State
three main types of error in measurement. Illustrate your answer with reference
to temperature measurement using a faulty mercury-in-glass thermometer
using a faulty mercury-in-glass thermometer. |
3
marks |
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The three main types of errors in measurement
are |
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| 1. |
personal errors |
arise from personal
bias or carelessness in reading an instrument. |
| 2. |
Random errors |
result from poor
sensitivity of the apparatus or unpredictable variations in experimental
situations. |
| 3. |
System errors |
are caused by the
incorrect use of instrument. |
|
1.5 |
|
In measuring temperature, if the student
reads 20oC instead of 30oC which is reported from
the thermometer, this is a personal error. If the thermometer is graduated
in 1oC, a reading with decimal place, for instance, 22.0oC
is considered to have a random error of 0.5oC. Finally, if the
thermometer is faulty, which always gives reading too high or too low,
the experiment is suffered from system error. |
1.5 |
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| b. |
State
the purpose of error estimation in data measurement, identifying the difference
between a precise measurement and an accurate measurement. |
3
marks |
|
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|
|
Error estimation tells how precise the
result is. This is mainly determined by the sensitivity or the precision
of the apparatus. |
1 |
|
A precise measurement is obtained from
an apparatus which could give a highly precise data. e.g. A reading of
12.23 m is more precise than a reading of 12.2 m. However, a precise data
may not be an accurate measurement. The accuracy of the final result is
determined by the method used (or procedures) and the reliability of the
apparatus. e.g. If a faulty thermometer giving a precise reading of 20.22oC
is not accurate. |
2 |
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| c. |
With
the aid of an example, explain why when two numbers are added, the largest
probable error of the sum is the sum of the largest probable errors of
the two numbers. |
4
marks |
|
|
|
|
The largest probable error is obtained
by considering the worst cases. |
1 |
|
Suppose the sum of the lengths of two
rods are to found. If the first rod is measured to be 12 ± 1 cm
and the other 50 ± 2 cm. There are two worst cases:
1. The actual lengths are the smallest,
i.e. 11 cm and 48 cm respectively. Then, the sum is 59 cm.
2. The actual lengths are the largest,
i.e. 13 cm and 52 cm respectively. Then, the sum is 65 cm.
The average of these two results is 62
cm. Both the worst cases deviate from the average value by 3 cm. This is
the final largest probable error, which is the sum of individual largest
probable error: 1 cm and 2 cm. |
3 |
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| d. |
By
stating the potential hazardous effects in using the following equipment
of apparatus, suggest three safety guidelines in handling each of them
i) a
laser tube |
6
marks |
|
|
|
|
A laser tube emits very strong beam of
light. If the laser is viewed directly, the retina of the eye would be
injured seriously. |
1 |
|
To avoid accident to happen, the laser
tube should never be pointed to anyone. A warning sign showing that laser
is in use in a room should be hoisted outside the room. When the laser
is not in used, it should be turned off. |
2 |
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ii)
a sealed radioactive source. |
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Radioactive substance emits radiations
(a, b
and g) which
are highly penetrating and could cause cancer after prolonged exposure. |
1 |
|
Radioactive substance should be kept inside
a box which is made of thick lead. The box should be kept safely inside
a cabinet with lock. Use a pair of special forceps to take it out for demonstration.
Return to the box immediately afterwards. |
2 |
|
A sealed radioactive source is a solid
radioactive source housed inside a metal case. Handle the source with great
care. Never allow the source to fall out from the case. |
* |
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