JEE Physics Units And Measurements MCQs Set 14

Answer: (a) [ML²T⁻²A⁻¹]

Explanation:
1. Flux = voltage × time (emf = dΦ/dt).
2. \( [V] \) = [ML²T⁻³A⁻¹], so [Φ] = [ML²T⁻²A⁻¹].

Teacher's Note:
1. The SI unit of flux is the weber.

Answer: (a) A/B

Explanation:
1. Only quantities of the same dimensions can be added, subtracted or equated.
2. Division and multiplication are allowed for any dimensions.

Teacher's Note:
1. Principle of homogeneity: every term in a valid equation has the same dimensions.

Answer: (c) A is true, but R is false.

Explanation:
1. Light year is a distance and a wavelength is a length, so the Assertion is true.
2. Both have the dimension of length, not time, so the Reason is false.

Teacher's Note:
1. Always find the dimension from the definition.

Answer: (b) A vernier callipers in which 10 vernier divisions match 9 main scale divisions, the main scale having 10 divisions in 1 cm

Explanation:
1. A reading 3.50 cm is stated to 0.01 cm, so the least count must be 0.01 cm = 0.1 mm.
2. Vernier: LC = 1 MSD − 1 VSD = 1 mm − 0.9 mm = 0.1 mm.
3. The metre scale has LC 0.1 cm, and the screw gauges have 0.01 mm and 0.02 mm.

Teacher's Note:
1. The number of decimal places in a reading shows the least count of the instrument.

Answer: (a) SI

Explanation:
1. MKS, CGS and FPS use only mass, length and time as base quantities.
2. SI has seven base quantities, including electric current, temperature, amount of substance and luminous intensity.

Teacher's Note:
1. SI has seven base units.
2. Systems built on mass, length and time alone are MKS, CGS and FPS.

Answer: (d) [ML⁰T⁻³]

Explanation:
1. Energy/(area × time) = [ML²T⁻²]/([L²][T]) = [MT⁻³].

Teacher's Note:
1. This is the same as intensity of radiation.

Answer: (a) 1.35 ± 1.48%

Explanation:
1. Mean = \( (1.34 + 1.38 + 1.32 + 1.36)/4 = 1.35 \).
2. Absolute deviations: 0.01, 0.03, 0.03, 0.01, mean 0.02.
3. Percentage error = \( (0.02/1.35) \times 100 \) = 1.48%.

Teacher's Note:
1. Find the mean first, then the mean of the absolute deviations.

Answer: (a) [ML⁻¹T⁻¹]

Explanation:
1. \( F \) = ηA(dv/dx), so η = F/(A·dv/dx) = [MLT⁻²]/([L²][T⁻¹]) = [ML⁻¹T⁻¹].

Teacher's Note:
1. The SI unit of viscosity is pascal second.

Answer: (d) I, II and III

Explanation:
1. No measurement is exact, so I is true.
2. Errors propagate to calculated results, so II is true.
3. Accuracy and precision are independent, so III is true.

Teacher's Note:
1. Precision is about repeatability; accuracy is about closeness to the true value.

Answer: (c) either positive or negative

Explanation:
1. A systematic error always acts in one direction for a given set-up, but it may make readings too high or too low.

Teacher's Note:
1. Zero error and instrument calibration errors are systematic; they can be corrected once known.

Answer: (d) A is false, but R is true.

Explanation:
1. The correct formula is \( T = 2\pi\sqrt{l/g} \). The dimensions of \( \sqrt{g/l} \) are \( T^{-1} \), not \( T \), so the given formula is wrong and the Assertion is false.
2. The Reason states the principle of homogeneity correctly and is true.

Teacher's Note:
1. Dimensional checking quickly exposes inverted formulae.

Answer: (b) 35.0 V

Explanation:
1. The factor with fewest significant figures is \( 3.23 A \), with three.
2. So \( V \) is rounded to three significant figures: \( 35.0 V \).

Teacher's Note:
1. In a product keep the least number of significant figures.

Answer: (b) momentum and Planck's constant

Explanation:
1. Momentum is [MLT⁻¹] and Planck's constant is [ML²T⁻¹], so they differ.
2. The others are equal: both stress and Young's modulus are pressure, and \( (\mu_{0}\varepsilon _{0})^{-1/2} \) is the speed of light.

Teacher's Note:
1. 1/√(μ₀ε₀) = \( c \) is a favourite dimensional identity.

Answer: (d) the sum of the relative errors

Explanation:
1. For \( Z = A/B, \DeltaZ/Z = \DeltaA/A + \DeltaB/B \), since errors add in the worst case.

Teacher's Note:
1. Relative errors add for both multiplication and division.

Answer: (d) [M⁰L⁰T⁻¹]

Explanation:
1. ω = angle/time. Angle is dimensionless, so \( [\omega] = [T^{-1}] \).

Teacher's Note:
1. Angular velocity and frequency have the same dimensions.

Answer: (a) 200.0 m

Explanation:
1. Count significant figures: 200.0 has 4, 20 × 10¹ has 2, 2 × 10² has 1, 0.2 × 10³ has 1.
2. More significant figures mean a smaller least count and greater accuracy.

Teacher's Note:
1. A trailing zero after a decimal point is significant.

Answer: (c) \( \frac{h}{ce^{2}} \)

Explanation:
1. [μ₀] = [MLT⁻²A⁻²].
2. Let μ₀ ∝ eᵃmᵇcᶜhᵈ with \( [e] \) = [AT]. Solving gives \( a = -2, b = 0, c = -1, d = 1 \).
3. So μ₀ ∝ h/(ce²).

Teacher's Note:
1. Check the answer by comparing dimensions of h/(ce²).

Answer: (b) frequency

Explanation:
1. \( [h] \) = [ML²T⁻¹] and \( [I] \) = [ML²].
2. \( h/I = [T^{-1}] \), the dimension of frequency.

Teacher's Note:
1. Use \( E \) = hf to get the dimension of \( h \).

Answer: (b) A-2, B-1, C-3, D-4

Explanation:
1. Length is measured with vernier callipers, volume with a burette, wire diameter with a screw gauge and mass with a common balance.

Teacher's Note:
1. Choose the instrument according to the required least count.

Answer: (b) 7

Explanation:
1. SI has seven base units: metre, kilogram, second, ampere, kelvin, mole and candela.

Teacher's Note:
1. Remember the seven: \( m \), kg, \( s, A, K \), mol, cd.
2. Radian and steradian are supplementary (dimensionless) units.

Answer: (a) Four

Explanation:
1. Leading zeros are not significant.
2. The digits 3, 0, 2, 6 are significant, so there are four.

Teacher's Note:
1. Zeros between non-zero digits count; zeros before the first non-zero digit do not.

Answer: (d) A-4, B-3, C-2, D-1

Explanation:
1. 1 fermi = \( 10^{-15} m, 1 \) AU = \( 1.496 \times 10^{11} m, 1 \) ly = \( 9.46 \times 10^{15} m, 1 \) parsec = \( 3.08 \times 10^{16} m \).

Teacher's Note:
1. Learn the four large and small length units together.

Answer: (b) [ML²T⁻²]

Explanation:
1. Torque = force × distance = [MLT⁻²][L] = [ML²T⁻²].

Teacher's Note:
1. Torque and energy share dimensions but differ in nature.

Answer: (c) lux

Explanation:
1. Illuminance is luminous flux per unit area, in lumen per square metre, which is called lux.

Teacher's Note:
1. Lumen measures luminous flux and candela measures luminous intensity.

Answer: (d) pressure if a = 1, b = −1, c = −2

Explanation:
1. Velocity is LT⁻¹ \( (a = 0, b = 1, c = -1) \) and force is MLT⁻² \( (a = 1, b = 1, c = -2) \); acceleration is LT⁻².
2. Pressure is ML⁻¹T⁻², which fits \( a = 1, b = -1, c = -2 \).

Teacher's Note:
1. Compare the exponents one by one.