PC01 — Units, Dimensions & Measurements

📗 CDS General Knowledge20 Questions · No Negative Marking

Question 1 of 20

Which of the following is NOT an SI base unit?

AKilogram BNewton CKelvin DAmpere

Newton is a derived SI unit (kg·m/s²), not a base unit. The 7 SI base units are: metre, kilogram, second, ampere, kelvin, mole, and candela. All other units are derived from these. Newton = force = mass × acceleration = kg·m/s².

Question 2 of 20

The dimensional formula of velocity is:

A[MLT⁻²] B[LT⁻¹] C[ML²T⁻²] D[MLT⁻¹]

Velocity = displacement/time = [L]/[T] = [LT⁻¹]. It has dimensions of length per time. Acceleration = [LT⁻²]; Force = [MLT⁻²]; Momentum = [MLT⁻¹]; Energy = [ML²T⁻²].

Question 3 of 20

Which physical quantity has the same dimensions as work?

APower BForce CTorque DPressure

Work = Force × distance = [MLT⁻²][L] = [ML²T⁻²]. Torque = Force × perpendicular distance = [MLT⁻²][L] = [ML²T⁻²]. Both have the same dimensions, though they are physically different (work is a scalar, torque is a vector). Power = [ML²T⁻³]; Pressure = [ML⁻¹T⁻²].

Question 4 of 20

The number of significant figures in the number 5.040 × 10³ is:

A2 B3 C4 D5

5.040 × 10³ has 4 significant figures: 5, 0, 4, and 0. The trailing zero after the decimal point IS significant. The zero between 5 and 4 (captive zero) is also significant. The ×10³ part does not affect significant figures.

Question 5 of 20

1 micrometre (μm) is equal to:

A10⁻³ m B10⁻⁶ m C10⁻⁹ m D10⁻¹² m

1 micrometre (μm) = 10⁻⁶ m. Prefixes: nano (n) = 10⁻⁹; micro (μ) = 10⁻⁶; milli (m) = 10⁻³; centi (c) = 10⁻²; kilo (k) = 10³; mega (M) = 10⁶; giga (G) = 10⁹. Cell size ~10 μm; wavelength of visible light ~400-700 nm.

Question 6 of 20

The dimensional formula [ML⁻¹T⁻²] corresponds to:

AForce BWork CPressure DMomentum

Pressure = Force/Area = [MLT⁻²]/[L²] = [ML⁻¹T⁻²]. Stress, elastic modulus (Young, Bulk, Shear), and energy density also have this dimensional formula. Force = [MLT⁻²]; Work = [ML²T⁻²]; Momentum = [MLT⁻¹].

Question 7 of 20

The least count of a vernier calliper with 50 vernier scale divisions coinciding with 49 main scale divisions (1 MSD = 1 mm) is:

A0.01 mm B0.02 mm C0.5 mm D0.1 mm

Least count = 1 MSD - 1 VSD. 1 VSD = 49/50 mm = 0.98 mm. LC = 1 - 0.98 = 0.02 mm. Standard vernier calipers (25 VSD = 24 MSD) give LC = 0.1/25... no: standard gives LC = 1/25 mm? Actually for 50 divisions on 49 MSD: LC = 1 - 49/50 = 1/50 mm = 0.02 mm. This is a high-precision vernier.

Question 8 of 20

Which of the following pairs have the same dimensional formula?

AAngular velocity and frequency BWork and power CVelocity and acceleration DForce and weight... actually force and impulse

Angular velocity ω = rad/s = [T⁻¹] (radians are dimensionless). Frequency f = Hz = cycles/s = [T⁻¹]. Both have the same dimensional formula [T⁻¹]. Work = [ML²T⁻²] vs Power = [ML²T⁻³] — different. Velocity [LT⁻¹] vs Acceleration [LT⁻²] — different.

Question 9 of 20

The principle of homogeneity of dimensions is used to:

AMeasure very small distances BCheck the dimensional correctness of equations CConvert units from one system to another DDetermine the charge on an electron

Dimensional analysis using the homogeneity principle: an equation is dimensionally correct only if both sides have the same dimensions. It can check equations, derive relationships between physical quantities, and convert units. It cannot determine dimensionless constants (like ½ in KE = ½mv²).

Question 10 of 20

A physical quantity that has dimensions [M⁻¹L³T⁻²] is:

APlanck constant BGravitational constant G CElectric charge DSpecific heat capacity

G = Fr²/m₁m₂ = [MLT⁻²][L²]/[M²] = [M⁻¹L³T⁻²]. Gravitational constant G = 6.674 × 10⁻¹¹ N·m²/kg². Planck constant h = [ML²T⁻¹]; Specific heat = [L²T⁻²K⁻¹].

Question 11 of 20

In an experiment, the measured value of a quantity is 5.32 ± 0.04. The percentage error is:

A0.04% B0.75% C4% D7.5%

Percentage error = (absolute error / measured value) × 100 = (0.04/5.32) × 100 = 0.752 ≈ 0.75%. This is the standard way to express experimental uncertainty as a percentage.

Question 12 of 20

The screw gauge (micrometer) has a least count of:

A1 mm B0.1 mm C0.01 mm D0.001 mm

Standard screw gauge: pitch = 1 mm (or 0.5 mm), 100 divisions on circular scale. LC = pitch/number of divisions = 1/100 = 0.01 mm. Some precision micrometers have 0.001 mm least count. The screw gauge is more precise than the vernier calliper (LC = 0.1 mm).

Question 13 of 20

Dimensions of the universal gas constant R are:

A[ML²T⁻²K⁻¹mol⁻¹] B[MLT⁻²K⁻¹] C[ML²T⁻²] D[M⁰L⁰T⁰]

From PV = nRT: R = PV/nT = [ML⁻¹T⁻²][L³]/[mol][K] = [ML²T⁻²K⁻¹mol⁻¹]. R = 8.314 J/mol·K. This combines energy dimensions [ML²T⁻²] with per-mole and per-kelvin.

Question 14 of 20

The dimensional formula of surface tension is:

A[MLT⁻²] B[MT⁻²] C[ML⁻¹T⁻²] D[ML⁰T⁻²]

Surface tension = Force/Length = [MLT⁻²]/[L] = [MT⁻²]. Also expressed as energy/area: [ML²T⁻²]/[L²] = [MT⁻²]. Unit: N/m or J/m². Note: [ML⁰T⁻²] = [MT⁻²] (same thing, just written explicitly showing L⁰).

Question 15 of 20

Error propagation: if Z = A × B, and errors in A and B are ΔA and ΔB respectively, then the relative error in Z is:

AΔA × ΔB BΔA/A - ΔB/B CΔA/A + ΔB/B D(ΔA + ΔB)/(A + B)

For products and quotients: relative errors ADD. ΔZ/Z = ΔA/A + ΔB/B. For Z = A^m × B^n: ΔZ/Z = m(ΔA/A) + n(ΔB/B). For Z = A + B: absolute errors add: ΔZ = ΔA + ΔB. For Z = A - B: ΔZ = ΔA + ΔB (still adds).

Question 16 of 20

The dimensional formula of coefficient of viscosity (η) is:

A[MLT⁻¹] B[ML⁻¹T⁻¹] C[ML⁻²T⁻¹] D[MT⁻¹]

From Stokes law F = 6πηrv: η = F/(6πrv) = [MLT⁻²]/([L][LT⁻¹]) = [ML⁻¹T⁻¹]. SI unit = Pa·s (pascal-second) = kg/(m·s). Also called dynamic viscosity. Water: ~0.001 Pa·s; Honey: ~10 Pa·s.

Question 17 of 20

Which of the following is a dimensionless quantity?

APressure BAngular momentum CRefractive index DImpulse

Refractive index n = speed of light in vacuum / speed in medium = [LT⁻¹]/[LT⁻¹] = dimensionless. Other dimensionless quantities: strain, specific gravity, coefficient of friction, angle (radians). Pressure = [ML⁻¹T⁻²]; Angular momentum = [ML²T⁻¹]; Impulse = [MLT⁻¹].

Question 18 of 20

One angstrom (Å) is equal to:

A10⁻⁸ m B10⁻¹⁰ m C10⁻¹² m D10⁻⁶ m

1 angstrom (Å) = 10⁻¹⁰ m = 0.1 nm. Used to express atomic and molecular dimensions: hydrogen atom radius ~0.53 Å; bond lengths ~1-3 Å. Named after Anders Jonas Angstrom. Wavelength of X-rays is in the angstrom range.

Question 19 of 20

The dimensional formula of electrical resistance is:

A[ML²T⁻³A⁻²] B[ML²T⁻²A⁻¹] C[MLT⁻²A⁻²] D[ML³T⁻³A⁻²]

R = V/I. V = W/q = [ML²T⁻²]/[AT] = [ML²T⁻³A⁻¹]. R = [ML²T⁻³A⁻¹]/[A] = [ML²T⁻³A⁻²]. SI unit = Ohm (Ω). This can also be derived from R = ρL/A using the dimensions of resistivity.

Question 20 of 20

The dimensional formula for Planck constant h is:

A[MLT⁻¹] B[ML²T⁻²] C[ML²T⁻¹] D[ML²T⁻³]

E = hν → h = E/ν = [ML²T⁻²]/[T⁻¹] = [ML²T⁻¹]. Planck constant h = 6.626 × 10⁻³⁴ J·s. It has the dimensions of angular momentum (action). This is the fundamental quantum of action in quantum mechanics.