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Published on: 29/05/2021
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Questions + Answers key
Take MCQ Physics Test1.
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 upper bound on the quantity).
The number of air molecules in your classroom
2.
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 upper bound on the quantity).
The number of strands of hair on our head
3.
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 upper bound on the quantity).
The mass of an speed during a storm
4.
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 upper bound on the quantity).
The total mass of rain-bearing clouds over India during the monsoon.
1.
The number of air molecules in your classroom
We measure the length(l), breadth (b) and height (h) of our classroom.
\(\therefore \) The volume of classroom = Volume of air in classroom
\(V=l\times b\times h\)
We know that at NTP, one mole of air occupies a volume of 22.4 L i.e., 22.4 x 10-3m3
Number of air molecules in one mole of air
= Avogadro number(N) = 6.023 x 1023
\(\therefore \) Number of air molecules in our classroom
\(=\frac { 6.023\times 10^{ 23 } }{ 22.4\times 10^{ -3 } } \times (l\times b\times h)\)
2.
The number of strands of hair on our head
If we assume a uniform distribution of strands of hair on head then, the number of strands of hair
= Area of the head/Area of cross-section of hair
The thickness of a strand of hair is measured by an appropriate instrument, if it is obtained
d = 5 x 10-5 = 5 x 10-3 cm
Then, area of cross-section of human hair
\(=\pi \left( \frac { d }{ 2 } \right) ^{ 2 }=\frac { \pi d^{ 2 } }{ 4 } \)
\(\\ =\frac { 3.14\times (5\times 10^{ -3 })^{ 2 } }{ 4 } =\frac { 3.14\times 25 }{ 4 } \times 10^{ -6 }cm^{ 2 }\)
Average radius of human head (r)=8 cm
\(\because \) Area of human head \(=\pi r^{ 2 }=3.14\times (8)^{ 2 }\)
3.14 x 64 cm2
\(\therefore \)The number of strands of hair \(=\frac { 3.14\times 64 }{ 3.14\times \frac { 25 }{ 4 } \times 10^{ -6 } } \)
\(\approx 10\times 10^{ 6 }=10^{ 7 }\)
3.
We can measure the mass of an elephant using the law of flotation. According to which, in floating condition the mass of an object dipped in a liquid is equal to the mass of the liquid displaced by the submerged part of the body in liquid. We take a boat of known base area A. Now, empty submerged part of the boat in water (d1 ) is measured.
The volume of water displaced by the boat (V1) = Ad1
\(\therefore \) Now move the elephant into this boat and again depth of the submerged part of the boat in water (d2) is measured.
The volume of water displaced by the boat elephant
V2 = Ad2
Volume of water displaced by the elephant
\(={ V }_{ 2 }-{ V }_{ 1 }={ Ad }_{ 2 }-{ Ad }_{ 1 }=A({ d }_{ 2 }-{ d }_{ 1 })\)
If is the density of water then, mass of the elephant
= mass of the water displaced by the elephant
= A(d2-d2)\(\rho \)
4.
The total mass of rain-bearing clouds over India during the monsoon
If meteorologist record 10 cm of average rainfall during monsoon then
Height of average rainfall (h) = 10 cm = 0.1 m
Area of India (A) = 3.3 million square km
= 3.3 x 106 square km [\(\because \) 1 million = 106]
= 3.3 x 106(103m)2
= 3.3 x 106 x 106m2 = 3.3 x 1012m2 [\(\because \) 1 km = 103]
Volume of rain water (V) = Area x height
= Axh = 3.3 x 1012m2 x 0.1m
=3.3x1011m3
Density of water (\(\rho \) ) = 103 kg/m3
Mass of rain water (m) = Volume x Density
= m = vx
= 3.3 x 1011m3 x 103 kg/m3
[Density = [\(\because \) mass/Volume]
= 3.3 x 1014 kg
Therefore, total mass of rain bearing clouds over India during the monsoon is 3.3 x 1014 kg.
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