NCERT Class 11 Physics Solutions: Chapter 2-Unit and Measurement Part 12

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Question: 2.21

Precise measurements of physical quantities are a need of science. For example, to ascertain the speed of an aircraft, one must have an accurate method to find its positions at closely separated instants of time. This was the actual motivation behind the discovery of radar in World War II. Think of different examples in modern science where precise measurements of length, time, mass etc. are needed. Also, wherever you can, give a quantitative idea of the precision needed.

Answer: 2.21

  • It is indeed very true that precise measurements of physical quantities are essential for the development of science. For example, ultra-shot laser pulses (time interval) are used to measure time intervals in several physical and chemical processes.

  • X-ray spectroscopy is used to determine the inter-atomic separation or inter-planer spacing.

  • The development of mass spectrometer makes it possible to measure the mass of atoms precisely.

Question: 2.22

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):

(A) The total mass of rain-bearing clouds over India during the monsoon

(B) The mass of an elephant

(C) The wind speed during a storm

(D) The number of strands of hair on your head

(E) The number of air molecules in your classroom.

Answer: 2.22


  • During monsoon, a metrologist records about 215 cm of rainfall in India i.e., the height of water column,

  • Area of country,

  • Hence, volume of rain water,

  • Density of water,

  • Hence, mass of rain water

  • Hence, the total mass of rain – bearing clouds over India is approximately


  • Consider a ship of known base area floating in the sea. Measure its depth in sea (say).

  • Volume of water displaced by the ship,

  • Now, move an elephant on the ship and measure the depth of the ship () in this case.

  • Volume of water displaced by the ship with the elephant on board,

  • Volume of water displaced by the elephant

  • Density of water

  • Mass of elephant


  • Wind speed during a storm can be measured by an anemometer. As wind blows, it rotates. The rotation made by the anemometer in one second gives the value of wind speed.


  • Area of the head surface carrying hair

  • With the help of screw gauge, the diameter and hence, the radius of a hair can be determined. Let it be r.

Area of one hair

  • Number of strands of hair

  • Let the volume of the room be V.

  • One mole of air at NTP occupies 22.4 i.e., volume.

  • Number of molecules in one mole

Number of molecules in room of volume V