Short & Long Answer Questions Units & Measurement - Physics for JEE Main & Advanced
Q1. What is the necessity of selecting some units as fundamental units
Ans. The number of physical quantities that can be measured is very large. If a separate unit were defined for each one, it would be impractical to remember and use them because they would be unrelated. Choosing a small set of fundamental units allows many other (derived) units to be formed from them in a consistent way.
Q2. How is SI a coherent system of units?
Ans. In the SI system, every derived unit can be obtained from the base (and supplementary) units by multiplying and dividing them without introducing any additional numerical factors. Because no extra conversion factors are needed when forming derived units from base units, SI is called a coherent system of units.
Q3. In defining the standard of length, (the prototype metre), we have to specify the temperature at which the measurement should be made. Are we justified in calling length a fundamental quantity, if another physical quantity (temperature) has to be specified in choosing a standard?
Ans. Yes. The choice of length as a fundamental quantity is justified because its modern definition is tied to atomic or electromagnetic standards (for example, the wavelength or the speed of light), which are not affected by ordinary laboratory temperature. Thus length remains a basic independent quantity even if an experimental prototype required a specified temperature in earlier definitions.
Q4. Do Å and AU stand for the same unit of length?
Ans. No. 1 Å (angstrom) = 10-10 m. 1 AU (astronomical unit) = 1.496 × 1011 m. They differ by many orders of magnitude and are used for very different length scales.
Q5. Why is it convenient to express the distances of stars in terms of light year rather than in metre or kilometre?
Ans. One light year = 9.46 × 1015 m = 9.46 × 1012 km. Since stellar distances are extremely large, using the light year gives numbers that are more manageable and easier to compare than metre or kilometre values.
Q6. Comment on the statement: "To define a physical quantity for which no method of measurement is given or known has no meaning."
Ans. The statement is not correct. A physical quantity must have a clear physical meaning, but it need not always be measurable directly. Many quantities are defined conceptually and are measured by indirect methods. Entropy is an example: it has a well-defined meaning and can be measured indirectly through measurable processes.
Q7. Is the measure of an angle dependent upon the unit of length?
Ans. θ (radian) = (Arc/Radius)
Because an angle (in radians) is the ratio of two lengths (arc length and radius), its numerical value is independent of the units chosen for length.
Q8. What is meant by angular diameter of the moon? What is its value
Ans.The angular diameter of the Moon is the angle subtended at an observer on Earth by two points at opposite ends of the Moon's diameter. Its value is about 0.5°.
Q9. For a given base line, which will show a greater parallax - a distant star or a nearby star?
Ans. Parallactic angle θ = base line / distance = b / S. Thus, for a fixed baseline b, the parallax is inversely proportional to the star's distance S. Therefore a nearby star shows a greater parallax than a distant star.
Q10. Why is parallax method not useful for measuring the distances of stars more than 100 light years away?
Ans.For stars beyond about 100 light years, the parallax angles become extremely small and fall below the limit of accurate measurement with usual instruments. Hence the parallax method is not practical for such distant stars.
Q11. What is the difference between mN, Nm and nm?
Ans. 1 mN = 1 milli newton = 10-3 newton (unit of force).
1 Nm = 1 newton metre (unit of torque or work, depending on context).
1 nm = 1 nanometre = 10-9 metre (unit of length).
Q12. Do all physical quantities have dimensions? If no, name three physical quantities which are dimensionless.
Ans.No. Some physical quantities are dimensionless. Examples are plane angle (radian), strain, and relative density (specific gravity).
Q13. If 'slap' times speed equals power, what will be the dimensional equation for 'slap'?
Ans. Given: slap × speed = power.
So, slap = power / speed.
[Power] = M L2 T-3; [Speed] = L T-1.
Therefore [slap] = (M L2 T-3) / (L T-1) = M L T-2.
The dimensions of slap are M L T-2, the same as those of force.
Q14. What is the basis of the principle of homogeneity of dimensions
Ans. The principle of homogeneity of dimensions is based on the fact that only physical quantities of the same kind can be added, subtracted or compared. Hence in any valid equation all terms must have the same dimensional formula.
Q15. If x = a + bt +ct2 where x is in metre and t in second; then what is the unit of c?
Ans.
[x] = [c t2].
So [c] = [x / t2].
Units of c = m s-2.
Q16. What are the dimensions of a and b in the relation: F =a+bx, where F is force and x is distance?
Ans.
[a] = [F] = M L T-2.
[b] = [F / x] = (M L T-2) / L = M T-2.
Q17. Name two physical quantities having the dimensions [ML2T-2].
Ans. Work (energy) and torque both have dimensions M L2 T-2.
Q18. Write three physical quantities having dimensions [ML-1T-1]
Ans. Coefficient of (dynamic) viscosity, momentum per unit area, impulse per unit area.
Q19. If the units of force and length each are doubled, then how many times would the unit of energy be affected?
Ans. Energy = force × length. If both force and length units are doubled, the unit of energy becomes 2 × 2 = 4 times larger. Thus the unit of energy increases by a factor of four.
Q20. The velocity v of a particle depends on time t as: υ=At2 + Bt + C where v is in m/s and t in second. What are the units of A, B and C?
Ans.
Unit of
A = (unit of v) / (unit of t2) = (m s-1) / s2 = m s-3.
Units of
B = (unit of v) / (unit of t) = (m s-1) / s = m s-2.
Unit of
C = unit of v = m s-1.
Q21. Can a quantity have dimensions but still has no units?
Ans. No. A quantity that has dimensions must have units for its measurement; without units the numerical measure cannot be expressed.
Q22. Can a quantity have different dimensions in different systems of units?
Ans.No. The dimensional formula of a physical quantity is independent of the system of units; it remains the same in all consistent systems of units.
Q23. Can a quantity have units but still be dimensionless?
Ans.Yes. A plane angle is dimensionless (ratio of two lengths) but is assigned the unit radian for measurement.
Q24. Does the magnitude of a physical quantity depend on the system of units chosen?
Ans.No. The physical magnitude (that is, the actual physical amount) of a quantity is independent of the system of units. Only its numerical value depends on the chosen units.
Q25. Justify L + L = L and L - L = L.
Ans.When two lengths are added, the result is a length; therefore L + L = L. Similarly when one length is subtracted from another, the result remains a length, so L - L = L. This follows from the fact that addition and subtraction of like physical quantities yield the same kind of quantity.
Q26. Can there be a physical quantity that has no units and no dimensions?
Ans.Yes. Strain (ratio of change in length to original length) is a physical quantity that is both unitless and dimensionless.
Q27. Can an instrument be called precise with-out being accurate? Can it be accurate without being precise?
Ans. Yes. An instrument can be precise (it gives very similar readings repeatedly) without being accurate (those readings may all be far from the true value). However, accurate measurements require the instrument to be both accurate and reasonably precise.
Q28. Which of the following length measurements is
(i) most precise and
(ii) least precise?
Give reason
(i) l = 5 cm
(ii) l = 5.00 cm
(iii) 5.000 cm
(iv) 5.000 cm
(v) 5.00000 cm.
Ans.
(i) The last measurement (5.00000 cm) is the most precise because it shows the greatest number of significant figures; it implies the measuring instrument has a least count of 0.00001 cm.
(ii) The first measurement (5 cm) is the least precise because it has only one significant figure and implies a least count of 1 cm.
Q29. Which of the following readings is the most accurate:
(i) 5000 m
(ii) 5×102 m
(iii) 5×103 m
Ans. All three readings have the same accuracy/precision because each has 1 significant figure. hence, all are equally accurate.
Q30. Which quantity in a given formula should be measured most accurately?
Ans.The quantity which appears with the highest power (exponent n) in the formula should be measured most accurately, because any fractional error in that quantity is multiplied by n in the result and therefore contributes most to the final error.
Q31. Which of the following measurements is more accurate and why?
(a) 0.0002 g
(b) 20.0 g
Ans. (b) 20.0 g is more accurate because it has more significant figures (3 s.f.) than 0.0002 g (1 s.f.), hence smaller relative error.
Q32. Why do we treat length, mass and time as basic or fundamental quantities in mechanics?
Ans.Length, mass and time are taken as fundamental in mechanics because:
(i) They represent basic physical measures from which other quantities are defined.
(ii) There are no simpler mechanical quantities from which these can be expressed.
(iii) They are independent of one another (none can be expressed in terms of the others).
(iv) Most other mechanical quantities (velocity, force, energy, etc.) can be derived from these three quantities.
Q33. SI is a rational system of units while mks system is not so. Justify.
Ans. SI is a rationalised system because its electromagnetic equations are written in a consistent form without introducing extra numerical factors, whereas in the older MKS system such extra factors appear irregularly, so SI is rational but MKS is not.
Q34. Why it became necessary to redefine metre on atomic standard?
Ans.Redefinition was necessary because the prototype metre bar had practical difficulties:
(i) It is difficult to preserve and maintain a single physical artefact as an absolute standard over long time.
(ii) Producing exact replicas for use worldwide is hard.
(iii) Replication techniques and environmental effects limit the achievable accuracy. An atomic or electromagnetic standard can be reproduced anywhere with higher stability and precision.
Q35. What are the advantages of defining metre in terms of the wavelength of light radiation?
Ans.The advantages are:
(i) It can be reproduced precisely anywhere and at any time.
(ii) It is invariant in time and space (fundamentally the same everywhere).
(iii) It is largely unaffected by environmental conditions like ordinary temperature and pressure.
(iv) It allows very high accuracy (for example, of order 1 part in 109 with modern techniques).
Q36. Give reasons why is platinum iridium alloy used in making prototype metre and kilogram.
Ans.Platinum-iridium alloy is used because:
(i) The alloy is little affected by temperature changes (low thermal expansion).
(ii) It is highly resistant to corrosion and wear, so standards remain stable.
(iii) It is hard and mechanically robust.
(iv) It is chemically stable and does not change with time under normal conditions.
Q37. What is the basic principle of alpha particle scattering method for estimating the size of the nucleus?
Ans.Both the α-particle and the nucleus carry positive charge, so they repel each other. As an α-particle approaches a nucleus, its kinetic energy converts into electrostatic potential energy. The distance of closest approach r0 is reached when the kinetic energy is entirely converted into potential energy. Equating the initial kinetic energy to the electrostatic potential energy at r0 gives an estimate of r0, which is of the order of the nuclear size.
Q38. What is common between bar and torr?
Ans.Both bar and torr are units of pressure.
1 bar ≈ 1 atmosphere ≈ 760 mm of Hg column.
1 torr = 1 mm of Hg column.
Therefore 1 bar ≈ 760 torr.
Q39. Distinguish between accuracy and precision.
Ans. Accuracy refers to how close a measured value is to the true or accepted value. Precision refers to the reproducibility of repeated measurements - how close the measurements are to each other. A set of measurements can be precise without being accurate, but accurate measurements should also be reasonably precise.
Q40. For the determination of "g" using a simple pendulum, measurements of l and T are required. Error in the measurement of which of these will have larger effect on the value of "g" thus obtained and why? What is done to minimize this error?
Ans.For a simple pendulum, g = (4π2 l) / T2. The time period T appears squared in the denominator, so a small fractional error in T produces about twice the fractional error in the calculated value of g compared with the same fractional error in l. Hence error in T affects g more. To minimise this error, the time for a large number of oscillations is measured and the mean period is obtained by dividing the total time by the number of oscillations; this reduces the relative timing error.
Q41. Magnitude of force F experienced by a certain object moving with speed υ is given by F=Kv2 , where K is a constant. Find the dimensions of K.
Ans.
From F = K v2, we get K = F / v2.
[F] = M L T-2; [v] = L T-1, so [v2] = L2 T-2.
Therefore [K] = (M L T-2) / (L2 T-2) = M L-1.
In SI units K has units kg m-1.
where T is time period, G is gravitational constant, M is mass and r is radius of orbit.
Ans.
(i) T2 = 4π2 r2
Dimensionally, LHS has dimension T2 while RHS has dimension L2. Since T2 ≠ L2, this formula is incorrect.
(ii)
Apply the same procedure: write dimensions of both sides and compare. If the dimensions do not agree, the relation is incorrect.
(iii)
Use [G] = M-1 L3 T-2. For the standard orbital relation T2 ∝ r3 / (G M), the RHS has dimensions:
[r3] / ([G][M]) = L3 / (M-1 L3 T-2 × M) = T2.
Thus the third relation (the one with r3/(GM)) is dimensionally consistent and therefore correct.
Ans. Standard practice is to round the reported measurement to the same decimal place as the quoted uncertainty. The uncertainty 0.11 s begins with 1 so two significant figures for the uncertainty are acceptable; it indicates precision up to the hundredths place (0.01 s). Therefore the mean period 2.825 s should be rounded to the hundredths place to match the uncertainty.
Rounding 2.825 to two decimal places gives 2.83 s. Thus the result should be reported as 2.83 ± 0.11 s.
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