UNITS AND MEASUREMENTS
Very Short Question Answers
Q1. Distinguish between accuracy and precision?
Ans.| Accuracy | Precision |
| 1) It measures closeness of the measured value to the true value of quantity. |
1) This is the limit up to which a quantity can be measured with the given instrument. |
| 2) It depends on error | 2) It does not depend on error. |
Q2. What are the different types of errors that can occur in a measurement?
Ans. i) Systematic errors: If the errors are always in one direction, then they are known as
systematic errors.
ii) Random errors: If the measured values differ from the true values irregularly both in
magnitude and sign, then these errors are known as random errors.
iii) Gross errors.
Q3. How systematic errors be minimised or eliminated?
Ans.- By improving experimental techniques.
- By selecting better instruments.
- By removing personal bias as far as possible.
Q4. Illustrate how the result of a measurement is to be reported indicating the error involved?
Ans. As every measurement contains errors, the result of a measurement is to be reported in
such a manner to indicate the precision of measurement.
Measurement = A ± ∆𝐴 (∆A = error)
Q5. What are significant figures and what do they represent when reporting the result of a measurement?
Ans. In the reported result of measurement the reliable digits plus the first uncertain digit are known as significant digits or significant figures.
They represent the precision of a measurement.
Q6. Distinguish between fundamental units and derived units?
Ans.| Fundamental units | Derived units |
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Q7. Why do we have different units for the same physical quantity?
Ans. To measure the same physical quantity we have different units because
- Depends on the magnitude of the physical quantity measured.
- Different systems of measurements used. Ex. M.K.S System, C.G.S system, F.P.S
system.
Q8. What is dimensional analysis?
Ans. Dimensional analysis is a method in which fundamental quantities are raised to suitable powers to express a physical quantity.
Ex: Force:
Q9. How many orders of magnitude greater is the radius of the atom as compared to that of the nucleus?
Ans. The radius of the atom
The radius of the nucleus
Hence, the radius of the atom is times greater than that of the nucleus.
Q10. Express unified atomic mass unit in kg?
Ans. th of the mass of carbon isotope
Unified atomic mass unit
Short Question Answers
Q1. The vernier scale of an instrument has 50 divisions which coincide with 49 main scale divisions. If each main scale division is 0.5 mm, then using this instrument what would be the minimum inaccuracy in the measurement of distance?
Q2. In a system of units the unit of force is 100N, unit of length is 10m and the unit of time is 100s. What is the unit of mass in this system?
Q3. The distance of a galaxy from Earth is of the order of10²?m . Calculate the order of magnitude of the time taken by light to reach us from the galaxy?
Q4. The Earth-Moon distance is about 60 Earth radius. What will be the approximate diameter of the Earth as seen from the Moon?
Q5. Three measurements of the time for 20 oscillations of a pendulum are given as 39.6 s,39.9 s and 39.5 s . What is the precision in the measurements?What is the accuracy of the measurements?
Q6. A new unit of length is chosen so that the speed of light in vacuum is 1 unit. If light takes 8 min and 20 s to cover this distance, what is the distance between the Sun and Earth in terms of the new unit?
Q7. A student measures the thickness of a human hair using a microscope of magnification 100. He makes 20 observations and finds that the average thickness (as viewed in the microscope) is 3.5 mm. What is the estimate of the thickness of hair?
Q8. The velocity of a body is given by V=At²+ Bt + C . If v and t are expressed in SI,what are the units of A, B and C?
problems
Q1. State the number of significant figures in the following:(a) 6729 (b) 0.024 ( ) 0.08240 (d) 6.032 (e)4.57 x10?
Q2. A stick has a length of 12.132 cm and another has a length of 12.4 cm. If the two sticks are placed end to end what is the total length? If the two sticks are placed side by side, what is the difference in their lengths?
Q3. Each side of a cube is measured to be 7.203 m. What is (i) The total surface area and (ii) The volume of the cube, to appropriate significant figures?
Q4. The error in measurement of radius of a sphere is 1%. What is the error in the measurement of volume?
Q5. The percentage error in the mass and speed are 2% and 3% respectively. What is the maximum error in kinetic energy calculated using these quantities?
Q6. One mole of an ideal gas at standard temperature and pressure occupies 22.4 L (molar volume). If the size of the hydrogen molecule is about what is the ratio of molar volume to the atomic volume of a mole of hydrogen?