83 free MCQs on Units and Measurements, each with its own worked answer and explanation. SI base units, dimensional analysis, significant figures, and error propagation. The toolkit every physics calculation relies on.
Take the timed Units and Measurements chapterwise test →83 practice questions on Units and Measurements, sorted Easy → Hard. Try each one first, then open its answer page for the worked explanation. Want the full theory first? Read the Units and Measurements notes.
The 7 SI base units. All derived units (newton, joule, watt, volt, etc.) can be expressed as combinations of these 7 fundamental units raised to various powers.
Q1.
The unit of plane angle, the radian, measures which of the following?
Q2.
One astronomical unit (AU), the mean Earth-Sun distance, is closest to:
Q3.
The prefix micro corresponds to a multiplying factor of:
Q4.
The SI base unit of luminous intensity is the:
Q7.
In the number 0.0025, how many significant figures are there?
Q8.
What is the dimensional formula of force?
Q9.
Which term describes the closeness of a measurement to the true value?
Q10.
If a measurement is repeated and gives values 9.8, 9.7, 9.9, 9.8, what is being assessed when these values are very close together?
Q11.
Which of these is a dimensionless unit?
Q12.
Which of the following is a fundamental (base) physical quantity in the SI system?
Q13.
The order of magnitude of the mass of an electron (about 9.1 × 10⁻³¹ kg) is best expressed as:
Q16.
The SI unit of mass is the:
Q18.
The number of base (fundamental) quantities in the SI system is:
Q19.
Which of the following is a derived unit?
Q20.
The SI unit of electric current is the:
Q21.
The SI unit of thermodynamic temperature is the:
Q22.
The prefix "kilo" represents a multiplying factor of:
Q24.
The SI unit of the amount of substance is the:
Q25.
From the steady conduction relation Q/t = kAΔT/L, the dimensional formula of the thermal conductivity k is:
Q26.
The dimensional formula of surface tension (force per unit length) is:
Q27.
The dimensional formula of the coefficient of viscosity is:
Q28.
The period of a pendulum is T = 2π√(L/g). If L is measured with 2% error and g with 3% error, the maximum percentage error in T is:
Q29.
The product 2.5 × 1.25, reported with the correct number of significant figures, is:
Q30.
Which physical quantity has the same dimensions as Planck's constant?
Q31.
The radius of a circle is measured with a relative error of 2%. What is the percentage error in its calculated area?
Q32.
Two resistances are measured as R<sub>1</sub> = 100 ± 3 Ω and R<sub>2</sub> = 200 ± 4 Ω. What is the absolute error in their series combination (R<sub>1</sub> + R<sub>2</sub>)?
Q33.
In the equation s = ut + (1/2)at², dimensional analysis is used to confirm the equation is correct because:
Q34.
A number is recorded as 3.50 × 10⁴ kg. How many significant figures does it have?
Q35.
A student measures the length of a rod as 25.5 cm using a scale with least count 0.1 cm. The percentage error in this measurement is closest to:
Q36.
The density of a cube is found by measuring its mass and the length of one side. If the mass has a relative error of 2% and the side length has a relative error of 1%, the relative error in the calculated density is:
Q37.
Which of the following pairs of physical quantities has the same dimensional formula?
Q38.
When adding the measured lengths 4.23 m, 1.2 m, and 0.234 m, the sum should be reported, following significant figure rules, as:
Q39.
The volume of a sphere is calculated from its measured diameter. If the diameter is measured with a relative error of 1.5%, the relative error in the calculated volume is:
Q40.
Which of these is an example of a derived unit being expressed entirely in terms of SI base units?
Q41.
The dimensional formula of force is:
Q42.
The dimensional formula of work or energy is:
Q43.
The dimensional formula of power is:
Q44.
The dimensional formula of linear momentum is:
Q45.
The dimensional formula of pressure is:
Q46.
Which pair of quantities has the same dimensions?
Q48.
The dimensional formula of velocity is:
Q49.
The dimensional formula of acceleration is:
Q50.
A physical quantity having magnitude but no direction is a:
Q51.
The frequency of vibration of a liquid drop is assumed to depend only on the surface tension S, the density ρ and the radius r. Dimensional analysis gives the frequency proportional to:
Q52.
In a new system the unit of force is 10 N, of length 5 m and of time 2 s. The unit of mass in this system equals:
Q53.
The dimensional formula of the Boltzmann constant k (energy per unit temperature) is:
Q54.
A vernier caliper has 20 vernier divisions coinciding with 19 mm on the main scale (main scale least count 1 mm). If the main scale reads 12 mm and the 6th vernier division coincides, the reading is:
Q55.
The escape velocity from a planet is assumed to depend only on surface gravity g and radius R. Dimensional analysis gives escape velocity proportional to:
Q56.
The period of oscillation of a simple pendulum is measured as T = 2π√(l/g). Why can dimensional analysis confirm the form l/g under the square root but not the factor of 2π?
Q57.
A physical quantity Z is calculated as Z = A²B³/C, where A, B, and C are measured with relative errors of 1%, 2%, and 3% respectively. What is the maximum percentage error in Z?
Q58.
A student measures the time period of a pendulum using a stopwatch with a least count of 0.1 s, timing 20 oscillations to get 36.0 s. If the same stopwatch were used to time only 5 oscillations instead, the percentage error in the measured time period would:
Q59.
In the formula for the viscous force F = 6πηrv (Stokes' law), η is coefficient of viscosity, r is radius, and v is velocity. If η is found by measuring F, r, and v with relative errors of 2%, 1%, and 2% respectively, the maximum relative error in η is:
Q60.
A new system of units is defined where the unit of mass is 2 kg, the unit of length is 2 m, and the unit of time is 2 s. What is the value of 16 J of energy in this new system?
Q61.
The Reynolds number Re, used to predict whether fluid flow is laminar or turbulent, is a dimensionless combination of fluid density ρ, velocity v, characteristic length L, and viscosity η. Which combination is dimensionally consistent with Re?
Q62.
A physical quantity X is given by X = (P²Q<sup>1/2</sup>)/(R³S²), where P, Q, R, S are measured with percentage errors of 3%, 2%, 1%, and 4% respectively. The percentage error in X is:
Q63.
Two quantities A and B have different dimensions. Which of the following operations can still be dimensionally valid?
Q64.
A measurement of the speed of light gives values 2.98 × 10<sup>8</sup>, 3.01 × 10<sup>8</sup>, 2.99 × 10<sup>8</sup>, and 3.02 × 10<sup>8</sup> m/s across four trials. Compared to the accepted value of 2.998 × 10<sup>8</sup> m/s, this data set best illustrates:
Q65.
A wire's resistance is calculated using R = V/I, where V and I are read off analog meters. The voltmeter reading is 5.0 ± 0.1 V and the ammeter reading is 2.0 ± 0.05 A. The resistance, with its absolute error, should be reported as:
Q66.
The principle of homogeneity of dimensions states that every term in a valid physical equation has the same:
Q67.
In the equation v² = u² + 2as, the term 2as has the dimensions of:
Q68.
If Z = A²B/C where A, B and C have percentage errors 1%, 2% and 3%, the maximum percentage error in Z is:
Q69.
The dimensional formula of the universal gravitational constant G is:
Q70.
The dimensional formula of Planck’s constant h is:
Q71.
Which of the following quantities is dimensionless?
Q72.
In a measurement, accuracy refers to how close the result is to the ___ value:
Q74.
If the percentage error in measuring the side of a cube is 1%, the percentage error in its volume is:
Q76.
The frequency f of a vibrating string depends on its length L, tension F, and linear mass density μ. Dimensional analysis gives f proportional to:
Q77.
A quantity P = a²b³/(√c·d). If percentage errors in a, b, c, d are 1%, 2%, 3%, 4%, the maximum percentage error in P is:
Q78.
A mass of 5.74 g occupies a volume of 1.2 cm³. The density reported with correct significant figures is:
Q79.
In the van der Waals equation (P + a/V²)(V − b) = RT, the dimensions of a/b are:
Q80.
The dimensional formula of ε₀E² (where E is electric field) is:
Q81.
Which combination of the reduced Planck constant ħ, gravitational constant G, and speed of light c has the dimension of time?
Q82.
A screw gauge has pitch 1 mm and 100 circular divisions. While measuring a wire, the main scale reads 4 mm and the 30th circular division coincides. If it has a negative zero error of 5 divisions, the corrected diameter is:
Q83.
If force F, velocity v, and time T are chosen as fundamental units, the dimensional formula of mass is:
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