Imagine a situation when a man wants to buy a red coloured shirt, so he goes to a store. The shopkeeper speaks only English. The man says, “Ureed qameesan ahmar allawn”. The shopkeeper says, “What?!” The man asked for a red colored shirt, but he said it in Arabic. Obviously, the shopkeeper couldn’t understand anything since it was not a standard language.
Similarly, there are many systems and units in place for measuring different quantities like length, area, mass, volume and other things. For example, an acre is a common way of representing area measurement in India. One acre is around 4046 square meters if you look at the metric system. So now you can guess how difficult it would be if there were no standard units and measurement.
Similarly temperature is measured in degree Celsius and the same unit of measurement cannot be used to measure the length of a rod. Each quantity has to be measured in its own way. Magnitude and the measurement varies along with the quantity. Hence the need for the units of measurement for each quantity arises.
International System of Units
The International System of Units or SI units defines standard units for measurement of all physical quantities. In principle, any physical quantity can be expressed in terms of seven base units.
The Seven Base Unit
Property
Unit
Symbol
Length
Meter
m
Mass
Kilogram
kg
Time
Second
s
Electric Current
Ampere
A
Temperature
Kelvin
K
Amount of Substance
Mole
mol
Luminous Intensity
Candela
cd
Derived Units
Apart from the base units, there are SI units of derived units. These are called as such because their value is determined based on one or more base units. Some examples are given below:
Frequency – Hertz (Hz); 1 Hz = 1 s-1
Power – Watt (W); 1 W = 1 kg·m2s−3
SI Unit Prefixes
The SI system utilizes a standard system of prefixes to the basic units that allow them to be more relevant to and descriptive of relative magnitude.
Prefixes are used to identify the multiples or the fractions of the original unit. There are 20 accepted prefixes.
The table below lists the standard prefixes for the SI units of measurement.
Important derived SI units
How to Write Roman Numerals 1 to 100?
Roman numerals 1 to 100 can be obtained by using any of the two given below methods:
Method 1: In this method, we break 65 into the least expandable form, write their respective roman letter and add/subtract them, i.e. 65 = 50 + 10 + 5 = L + X + V = LXV
Method 2: In this method, we consider the groups of numbers for addition such as: 65 = 60 + 5 = LX + V = LXV
Rules to Write Roman Numerals from 1 to 100-
Certain rules are to be followed while writing roman numbers from 1 to 100. These rules are explained here in detail.
When a bigger letter precedes a smaller letter, the letters are added. For example: CX, C > X, so CX = C + X = 100 + 10 = 110.
When a smaller letter precedes a bigger letter, the letters are subtracted. For example: IV, I < V, so IV = V – I = 5 – 1 = 4.
When a letter is repeated multiple times, they get added. For example: MMM = M + M + M = 1000 + 1000 + 1000 = 3000
The same letter cannot be used more than three times in succession. V, L, and D cannot be repeated, they appear only once.
Write the answer of the following questions.
The magnitude of any physical quantity: A. Depends on the method of measurement B. Does not depend on the method of measurement C. Is more in S.I. system than in CGS system D. Directly proportional to the fundamental units of mass, length, and time
What is the unit of measurement of solid angle? A. Steradian B. Degrees C. Radians D. Grades
Newton-second is the unit of A. Velocity B. Angular Momentum C. Momentum D. Energy
Which of the following is not the unit of energy. A. Calorie B. Joule C. Electron volt D. Watt
Candela is the unit of: A. Electric intensity B. Luminous intensity C. Sound intensity D. None of these
Universal time is based on: A. Rotation of the earth on its axis B. Earth’s orbital motion around the earth C. Vibrations of cesium atom D. Oscillations of quartz crystal
Which of the following quantities has the same dimensions as that of energy? A. Power B. Force C. Momentum D. Torque
Which of the following pairs does not have similar dimensions? A. Stress and Pressure B. Tension and Surface Tension C. Planck’s Constant and Angular Momentum D. Angle and Strain
Which pair has the same dimensions? A. Work and Power B. Density and Relative Density C. Momentum and Impulse D. Stress and Strain
A unitless quantity: A. May have a non-zero dimension B. Always has a non-zero dimension C. Never has a non-zero dimension D. Does not exist
The ratio of the dimensions of Planck’s constant and that of moment of inertia has the dimensions of: A. Frequency B. Velocity C. Time D. Angular momentum
The dimension of Planck’s constant equals to that of: A. Energy B. Momentum C. Angular momentum D. Power
The physical quantities not having same dimensions are:| A. Pressure and Bulk modulus B. Torque and work C. Momentum and Planck’s constant D. Stress and Young’s modulus
In the C.G.S. system the magnitude of the force is 100 dyne. In another system where the fundamental physical quantities are kilogram, metre, and minute, the magnitude of the force is: A. 0.036 B. 0.36 C. 3.6 D. 36
Assertion (1): The method of dimensional analysis cannot validate the exact relationship between physical quantities in any equations.
Reason (R): It does not distinguish between the physical quantities having same dimensions.
A. Assertion (1) is true, Reason (R) is true; Reason ® is a correct explanation for Assertion (1). B. Assertion (1) is true, Reason (R) is true; Reason ® is not a correct explanation for Assertion (1). C. Assertion (1) is true, Reason (R) is false. D. Assertion (1) is false, Reason (R) is true.
If L = 2.331 cm, B = 2.1 cm, then L + B =? A. 4.431 cm B. 4.43 cm C. 4.4 cm D. 4 cm
Taking into account of the significant figures, what is the value of 9.99 m − 0.0099 m? (2020) A. 9.98 m B. 9.980 m C. 9.9 m D. 9.9801 m
If 97.52 is divided by 2.54, the correct result in terms of significant figures is: A. 38.4 B. 358.3937 C. 38.394 D. 38.39
A silver wire has mass (0.6 ± 0.006)g, radius (0.5 ± 0.005) mm and length (4 ± 0.04)cm. The maximum percentage error in the measurement of its density will be: A. 4% B. 3% C. 6% D. 7%
The mean time period of the second pendulum is 2.00s and the mean absolute error in the time period is 0.05s. To express the maximum estimate of error, the time period should be written as: A. (2.00 ± 0.01)s B. (2.00 + 0.025)s C. (2.00 ± 0.05)s D. (2.00 ± 0.10)s
A thin copper wire of length l metre increases in length by 2% when heated through 10°C. What is the percentage increase in the area when a square copper sheet of length l metre is heated through 10°C? A. 4% B. 8% C. 16% D. None of the above
The period of oscillation of a simple pendulum in the experiment is recorded as 2.63 s, 2.56 s, 2.42 s, 2.71 s and 2.80 s respectively. The average absolute error is: A. 0.1 s B. 0.11 s C. 0.01 s D. 1.0 s
Accuracy of measurement is determined by: A. Absolute Error B. Percentage Error C. Both D. None of these
The length of a cylinder is measured with a meter rod having the least count of 0.1 cm. Its diameter is measured with vernier calipers having the least count of 0.01 cm. Given that the length is 5.0 cm. and the radius is 2.0 cm. The percentage error in the calculated value of the volume will be: A. 1% B. 2% C. 3% D. 4%
In vernier calipers, one main scale division is x cm and the n division of the vernier scale coincides with (n – 1) divisions of the main scale. The least count (in cm) of the calipers is: A. (n – 1/n) x B. nx/(n – 1) C. x/n D. x/(n – 1)
A vernier caliper has 1 mm marks on the main scale. It has 20 equal divisions on the vernier scale which match with 16 main scale divisions. For this vernier caliper, the least count is: A. 0.02 mm B. 0.05 mm C. 0.1 mm D. 0.2 mm
If n main scale divisions coincide with (n + 1) vernier scale divisions. The least count of vernier calipers, when each centimetre on the main scale is divided into five equal parts, will be: A. 2n/(n+1) mm B. 2/(n+1) mm C. 1/2n mm D. 1/5n mm
The least count of the main scale of a screw gauge is 1mm. The minimum number of divisions on its circular scale required to measure 5mm diameter of wire is: A. 200 B. 50 C. 500 D. 100
Value of one main scale division is 1mm and 0.9 mm is value of one division of vernier scale, then vernier constant is: A. 0.9mm B. 1 mm C. 0.1 mm D. 0.8 mm
One centimetre on the main scale of vernier caliper is divided into ten equal parts. If 10 divisions of vernier scale coincide with 8 small divisions of the main scale, the least count of the caliper is A. 0.01 cm B. 0.02 cm C. 0.05 cm D. 0.005 cm