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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
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.
Write true or false.
Every measurement involves two things – a number and a unit.
What are the S.I. units of
- mass
- length
- time and
- temperature.
Write their names and symbols.
Exercise
Complete the analogy.
Height of a person: cm :: Length of your sharpened pencil lead:______?
Rulers, measuring tapes and metre scales are used to measure ______
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.
Which line is longer? C or D? Measure each line. How good is your guess?
What is Dinesh’s height in metres? _____ m _____ cm.
How wide is the rectangle? ________ cm
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 stand in their square? How many?
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.
- A longer boundary around the lake will help more birds to lay their eggs. So which lake should be kept for birds? Which lake should be used for boats?
What is the unit of measurements of very small lengths?
The Unit used to measure length ______.
Larger unit for measuring time is ______.
The radius of atom is of the order of 1 Å and the radius of nucleus is of the order of fermi. How many magnitudes higher is the volume of atom as compared to the volume of nucleus?
- The earth-moon distance is about 60 earth radius. What will be the diameter of the earth (approximately in degrees) as seen from the moon?
- Moon is seen to be of (½)°diameter from the earth. What must be the relative size compared to the earth?
- From parallax measurement, the sun is found to be at a distance of about 400 times the earth-moon distance. Estimate the ratio of sun-earth diameters.
In an experiment to estimate the size of a molecule of oleic acid 1 mL of oleic acid is dissolved in 19 mL of alcohol. Then 1 mL of this solution is diluted to 20 mL by adding alcohol. Now 1 drop of this diluted solution is placed on water in a shallow trough. The solution spreads over the surface of water forming one molecule thick layer. Now, lycopodium powder is sprinkled evenly over the film and its diameter is measured. Knowing the volume of the drop and area of the film we can calculate the thickness of the film which will give us the size of oleic acid molecule.
Read the passage carefully and answer the following questions:
- Why do we dissolve oleic acid in alcohol?
- What is the role of lycopodium powder?
- What would be the volume of oleic acid in each mL of solution prepared?
- How will you calculate the volume of n drops of this solution of oleic acid?
- What will be the volume of oleic acid in one drop of this solution?
Why is Earth's orbit used instead of its diameter to measure distances to stars using the parallax method?
In the parallax formula D = b/θ, what must be true about the angle θ for the calculation to be correct?
