Advertisements
Advertisements
Question
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.
Advertisements
Solution 1
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 ∼ 10–15 s) 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.
Solution 2
Extremely precise measurements are needed in modem science. As an example, while launching a satellite using a space launch rocket system we must measure time to a precision of 1 micro second. Again working with lasers we require length measurements to an angstrom unit (1 A° = 10-10m) or even a fraction of it. For estimating nuclear sizes we require a precision of 10-15 m. To measure atomic masses using mass spectrograph we require a precision of 10-30kg and so on.
RELATED QUESTIONS
Round up the following upto three significant figures:
34.216
The relative density of lead is 11.3. Its density is ______ g cm–3or ______ kg m–3.
The mean diameter of a thin brass rod is to be measured by vernier callipers. Why is a set of 100 measurements of the diameter expected to yield a more reliable estimate than a set of 5 measurements only?
The length, breadth, and thickness of a rectangular sheet of metal are 4.234 m, 1.005 m, and 2.01 cm respectively. Give the area and volume of the sheet to correct significant figures.
A man walking briskly in rain with speed v must slant his umbrella forward making an angle θ with the vertical. A student derives the following relation between θ and v: tan θ = v and checks that the relation has a correct limit: as v →0, θ → 0, as expected. (We are assuming there is no strong wind and that the rain falls vertically for a stationary man). Do you think this relation can be correct? If not, guess the correct relation.
A SONAR (sound navigation and ranging) uses ultrasonic waves to detect and locate objects under water. In a submarine equipped with a SONAR the time delay between generation of a probe wave and the reception of its echo after reflection from an enemy submarine is found to be 77.0 s. What is the distance of the enemy submarine? (Speed of sound in water = 1450 m s–1).
State the number of significant figures in the following:
0.007 m2
State the number of significant figures in the following:
0.0006032 m2
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 wind speed during a storm
Describe what is meant by significant figures.
Write a short note on the following.
Rounding - off
How many significant figures should be present in the answer of the following calculations?
`(2.5 xx 1.25 xx 3.5)/2.01`
Taking into account of the significant figures, what is the value of 9.99 m – 0.0099 m?
The mass and volume of a body are 4.237 g and 2.5 cm3, respectively. The density of the material of the body in correct significant figures is ______.
The length and breadth of a rectangular sheet are 16.2 cm and 10.1cm, respectively. The area of the sheet in appropriate significant figures and error is ______.
Using the rules for significant figures, the correct answer for the expression `(0.02858 xx 0.112)/(0.5702)` will be ______.
How many significant figures are present in the measurement 2007 grams?
Which of the following measurements contains exactly two significant figures?
What is the least count of a measuring instrument?
A length L is measured as 125 m, which is also written as 12500 cm and 125000 mm. How many significant figures does this measurement have?
