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Question
Just as precise measurements are necessary in science, it is equally important to be able to make rough estimates of quantities using rudimentary ideas and common observations. Think of ways by which you can estimate the following (where an estimate is difficult to obtain, try to get an upper bound on the quantity):
the number of strands of hair on your head
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Solution 1
Area of the head surface carrying hair = A
With the help of a screw gauge, the diameter and hence, the radius of a hair can be determined. Let it be r.
∴Area of one hair = πr2
Number of strands of hair `~~ "Total surface area"/("Area of one hair"pi) = A/r^2`
Solution 2
Let us assume that the man is not partially bald. Let us further assume that the hair on the head are uniformly distributed. We can estimate the area of the head. The thickness of a hair can be measured by using a screw gauge. The number of hair on the head is clearly the ratio of the area of head to the cross-sectional area of a hair.
Assume that the human head is a circle of radius 0.08 m i.e., 8 cm. Let us further assume that the thickness of a human air is 5 x 10-5m.
Number of hair on the head =Area of the head/Area of cross – section of a hair
=π (0.08)2/π(5 x 10-5)=64 x 10-4/25 x 10-10=2.56 x 106
The number of hair on the human head is of the order of one million.
RELATED QUESTIONS
The principle of ‘parallax’ in section 2.3.1 is used in the determination of distances of very distant stars. The baseline AB is the line joining the Earth’s two locations six months apart in its orbit around the Sun. That is, the baseline is about the diameter of the Earth’s orbit ≈ 3 × 1011m. However, even the nearest stars are so distant that with such a long baseline, they show parallax only of the order of 1” (second) of arc or so. A parsec is a convenient unit of length on the astronomical scale. It is the distance of an object that will show a parallax of 1” (second) of arc from opposite ends of a baseline equal to the distance from the Earth to the Sun. How much is a parsec in terms of meters?
Exercise
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- A
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Gold wire for B = _________ metres - C
Gold wire for C = __________ metres
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- D
So he will get __________ metres of gold wire!!
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- What is the length of the boundary of lake B in the drawing?
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