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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
Write true or false.
Every measurement involves two things – a number and a unit.
Fill in the blank.
In the ............ system, length is measured in centimetres.
Exercise
Ten millimetre makes one centimetre.
While measuring the length of a sharpened pencil, the reading of the scale at one end is 2.0 cm and at the other end is 12.1 cm. What is the length of the pencil?
Fill in the following chart.
| Property | Definition | Basic Unit | Instrument used for measuring |
| Length | |||
| Mass | |||
| Volume | |||
| Time |
Match the following.
| 1. | Length | kelvin |
| 2. | Mass | metre |
| 3. | Time | kilogram |
| 4. | Temperature | second |
Assertion (A): Distance between two celestial bodies is measured in terms of light year.
Reason (R): The distance travelled by the light in one year is one light year.
Measure the yellow rectangle. It is ________ cm long.
How many stamps can be placed along its length?
The fencing of a square garden is 20 m in length. How long is one side of the garden?
What formula is used to measure the area of your classroom?
What is the unit of measurements of very small lengths?
The Unit used to measure length ______.
To measure the distance of a planet from the earth, ______ method is used.
The distance of a galaxy is of the order of 1025 m. Calculate the order of magnitude of time taken by light to reach us from the galaxy.
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?
According to the modern definition, what fraction of a second does light travel to define one metre?
