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प्रश्न
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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उत्तर १
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`
उत्तर २
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.
संबंधित प्रश्न
The farthest objects in our Universe discovered by modern astronomers are so distant that light emitted by them takes billions of years to reach the Earth. These objects (known as quasars) have many puzzling features, which have not yet been satisfactorily explained. What is the distance in km of a quasar from which light takes 3.0 billion years to reach us?
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?
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 air molecules in your classroom.
Numerical Problem.
Inian and Ezhilan argue about the light year. Inian tells that it is 9.46 × 1015 m and Ezhilan argues that it is 9.46 × 10 12 km. Who is right? Justify your answer.
Guess whose tail is the longest. Now measure the tails. How good is your guess?
Now cut strips of equal sizes out of it. Using tape join the strips, end to end, to make a belt.
How long is your belt? _________
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- How many of you can sit in one square meter?
You can play this game on the ground. Make two squares of one square meter each. Divide your class into two teams. Ready to play!
- How many of you can stand in it?
You can play this game on the ground. Make two squares of one square meter each. Divide your class into two teams. Ready to play!
- Which team could make more children sit in their square? How many?
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- How much wire in all will the three need?
There are two beautiful lakes near a village. People come for boating and picnics in both the lakes. The village Panchayat is worried that with the noise of the boats the birds will stop coming. The Panchayat wants motorboats in only one lake. The other lake will be saved for the birds to make their nests.
- How many cm is the length of the boundary of lake A in the drawing?(use thread to find out)
Length is a fundamental quantity.
Match the following:
| Prefix | Symbol | ||
| a. | Centi | i. | k |
| b. | Nano | ii. | c |
| c. | Mili | iii. | n |
| d. | Kilo | iv. | m |
What is the unit of measurements of very small lengths?
What is the unit of measurements of very small lengths?
The distance between one end and the other end is called ______.
The Unit used to measure length ______.
According to the modern definition, what fraction of a second does light travel to define one metre?
Why is Earth's orbit used instead of its diameter to measure distances to stars using the parallax method?
