Notes
Physical Quantities — 30 MCQs
Precision and significant figures, dimensions and uses of dimensional analysis. Covers foundational concepts, applied reasoning and derivations.
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1. Which of the following is a fundamental physical quantity?
easyExplanation: Mass is a fundamental quantity independent of others. Velocity, force and pressure are derived quantities. -
2. The number of significant figures in 0.00420 is:
easyExplanation: Leading zeros are not significant; only 4, 2 and 0 are significant, giving 3 significant figures. -
3. Precision of a measurement primarily depends on:
easyExplanation: Precision is determined by the instrument's ability to resolve fine differences, which is the least count. -
4. A set of repeated measurements cluster tightly together but are far from the true value. This measurement is:
easyExplanation: Close clustering means precision; distance from true value means lack of accuracy. This is a systematic error. -
5. Trailing zeros in a number without a decimal point (e.g. 4500) are:
easyExplanation: Ambiguous; use scientific notation to clarify: 4.5 × 10³ (2 SF) or 4.50 × 10³ (3 SF). -
6. The dimensional formula of velocity is:
easyExplanation: Velocity = displacement / time, so [v] = [L] / [T] = [M⁰L¹T⁻¹]. -
7. Which base dimension symbol represents electric current in the SI system?
easyExplanation: [A] stands for ampere, the SI unit of electric current. -
8. The dimensional formula [M¹L²T⁻²] represents:
easyExplanation: Work = force × displacement = [MLT⁻²][L] = [ML²T⁻²]. Energy has the same dimension. -
9. According to the principle of homogeneity, an equation is dimensionally correct only if:
easyExplanation: Only quantities with identical dimensions can be added, subtracted or equated. -
10. When rounding 7.25 to 3 significant figures using the "round half to even" rule, the result is:
easyExplanation: When exactly halfway, round to the nearest even digit: 7.2 is even. -
11. In the addition 15.62 + 2.3, the result should be reported to:
mediumExplanation: For addition, match the least number of decimal places. 2.3 has 1 decimal place, so result = 17.9 (1 d.p.). -
12. In the multiplication 4.56 × 1.4, the result should be reported to:
mediumExplanation: For multiplication, match the least number of significant figures. 1.4 has 2 SF, so result = 6.4. -
13. Two physical quantities can be added together only if they have:
mediumExplanation: Only quantities with the same dimensions (e.g. both lengths) can be meaningfully added. -
14. Which of the following pairs of physical quantities have the same dimensional formula?
mediumExplanation: Both work and torque have dimension [ML²T⁻²], though they represent different physical concepts. -
15. A student reports the length of a rod as 12.300 cm using a vernier calliper. The number of significant figures is:
mediumExplanation: All five digits are significant: 1, 2, 3, 0 and 0 (trailing zero after decimal point). -
16. Dimensional analysis fails to derive relations involving:
mediumExplanation: Dimensional analysis handles products and powers, but cannot derive formulas with sums of different types of terms. -
17. The equation s = ut + ½at² is checked using dimensional analysis. What is the dimension of each term on the right-hand side?
mediumExplanation: [ut] = [LT⁻¹][T] = [L] and [½at²] = [LT⁻²][T²] = [L]. Both equal [s]. -
18. Which of the following CANNOT be determined using dimensional analysis alone?
mediumExplanation: Dimensional analysis cannot determine dimensionless constants like 2π, ½ or numerical coefficients. -
19. A physical quantity Q is assumed to depend on quantities X, Y, and Z as Q = k X^a Y^b Z^c. The values of a, b, c are found by:
mediumExplanation: Write both sides with dimensional formulas, then equate the exponents of each base dimension. -
20. Converting a physical quantity from one system of units to another using dimensional analysis relies on the fact that:
mediumExplanation: A physical quantity is invariant; only the numerical value and unit change, maintaining the same dimension. -
21. Using dimensional analysis, the time period T of a simple pendulum of length l in a gravitational field g is found to be proportional to:
hardExplanation: Assuming T = k l^a m^b g^c and equating powers gives a = ½, b = 0, c = −½, so T ∝ √(l/g). -
22. In the pendulum derivation T = k · l^a m^b g^c, equating the power of mass M on both sides gives:
hardExplanation: On the left, [T] has M⁰. On the right, only m carries M, so b must be 0 for dimensions to match. -
23. If the viscous force F on a sphere is assumed to depend on viscosity η, velocity v, and radius r as F = k η^a v^b r^c, the power of mass M in [η] = [ML⁻¹T⁻¹] directly fixes:
hardExplanation: F has [M¹L¹T⁻²]. Only η carries M, so a = 1 is required for the M exponent to balance. -
24. For the Stokes' law derivation (F = k η^a v^b r^c), solving the power equations gives the final relation:
hardExplanation: Equating M, L, T powers yields a = 1, b = 1, c = 1, so F = k η v r. -
25. A quantity Q depends on four independent physical quantities. Using only [M], [L], [T] as base dimensions, dimensional analysis to find Q's formula will:
hardExplanation: Four unknowns (the powers) but only three independent equations (M, L, T) means the system is underdetermined. -
26. The length of a wire is measured as 25.4 cm using a metre scale (least count 0.1 cm) and as 25.38 cm using a vernier calliper (least count 0.01 cm). Which statement is correct?
hardExplanation: Vernier has smaller least count, so it provides more precision (finer resolution). -
27. A rectangular plate has length 8.42 cm and breadth 3.7 cm, both measured experimentally. Its area, reported with the correct number of significant figures, should be:
hardExplanation: Area = 8.42 × 3.7 = 31.154 cm². Since 3.7 has 2 SF, round to 2 SF: 31 cm². -
28. Which of the following equations is dimensionally INCORRECT, given v = velocity, r = radius, T = time period, and g = acceleration due to gravity?
hardExplanation: [gr²] = [LT⁻²][L²] = [L³T⁻²] ≠ [L²T⁻²] = [v²]. This equation fails dimensional analysis. -
29. A student proposes the formula E = mc for the energy E of a particle of mass m moving with speed c, instead of E = mc². Using dimensional analysis, this proposed formula:
hardExplanation: [mc] = [M][LT⁻¹] = [MLT⁻¹], which is momentum, not energy [ML²T⁻²]. -
30. The centripetal force F on a body of mass m moving with speed v in a circle of radius r is assumed to be F = k · m^a v^b r^c. Using dimensional analysis, the derived relation is:
hardExplanation: Equating powers of M, L, T yields a = 1, b = 2, c = −1, giving F = kmv²/r.