Match List-I with List-II:
List-IList-II
(A) Angular Impulse(I) [M^0L^2T^-2]
(B) Latent Heat(II) [M L^2T^-3A^-1]
(C) Electrical resistivity(III) [M L^2T^-1]
(D) Electromotive force(IV) [M L^3T^-3"A^-2]
Choose the correct answer from the options given below:

Solution & Explanation

### Related Formula * **Angular Impulse** = Change in Angular Momentum = tau cdot Delta t = [M L^2 T^-2] cdot [T] = [M L^2 T^-1] [cite: 670, 672] * **Latent Heat** (L) = fracQm = frac[M L^2 T^-2][M] = [M^0 L^2 T^-2] * **Electrical resistivity** (\rho) = fracR cdot Al = frac[M L^2 T^-3 A^-2] cdot [L^2][L] = [M L^3 T^-3 A^-2] * **Electromotive force** (V) = fracWq = frac[M L^2 T^-2][A T] = [M L^2 T^-3 A^-1] ### Core Logic By comparing the formulas derived for each physical quantity with the options given in List-II [cite: 670, 673, 674]: * (A) matches with (III) [cite: 670, 672] * (B) matches with (I) * (C) matches with (IV) * (D) matches with (II) Hence, the correct matching is (A)-(III), (B)-(I), (C)-(IV), (D)-(II). ### Pattern Recognition In match-the-column dimensional analysis questions, identifying even one or two straightforward quantities like Latent Heat (L = Q/m) often immediately eliminates three incorrect options, securing a quick correct answer. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 11 Physics: Units and Measurements

Reference Study Guides

More Units and Measurements Previous-Year Questions — Page 6

Q44 jee_main_2024_01_february_morning Error Analysis
The radius (r), length (l) and resistance (R) of a metal wire was measured in the laboratory as: r = (0.35 pm 0.05)mathrm~cm R = (100 pm 10)mathrm~Omega l = (15 pm 0.2)mathrm~cm The percentage error in resistivity of the material of the wire is:
  • A. 25.6%
  • B. 39.9%
  • C. 37.3%
  • D. 35.6%

Solution

### Related Formula Resistivity formula: rho = RfracAl = Rfracpi r^2l Maximum relative error equation: fracDeltarhorho = fracDelta RR + 2fracDelta rr + fracDelta ll ### Core Logic Substitute the measured fractions: fracDeltarhorho = frac10100 + 2left(frac0.050.35right) + frac0.215 fracDeltarhorho = frac110 + 2left(frac17right) + frac175 fracDeltarhorho = 0.1 + 0.2857 + 0.0133 = 0.399 ### Step 1: Convert to Percentage \% severance = 0.399 times 100\% = 39.9\% ### Pattern Recognition The power of 2 in r^2 doubles its fractional error impact, making it the most dominant source of error in this setup. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 11 Physics: Units and Measurements Class 12 Physics: Current Electricity
Q45 jee_main_2024_01_february_morning Dimensional Analysis
The dimensional formula of angular impulse is:
  • A. [mathrmM mathrmL^-2mathrmT^-1]
  • B. [mathrmM mathrmL^2mathrmT^-2]
  • C. [mathrmM mathrmL mathrmT^-1]
  • D. [mathrmM mathrmL^2mathrmT^-1]

Solution

### Related Formula Angular Impulse equation: textAngular Impulse = int tau \, dt = Delta L textAngular Momentum (L) = mvr ### Core Logic By the impulse-momentum theorem for rotation, angular impulse equals the net change in angular momentum. Extract dimensions from [mvr]: [m] = [mathrmM] [v] = [mathrmLmathrmT^-1] [r] = [mathrmL] ### Step 1: Combine Dimensions [textAngular Impulse] = [mathrmM] times [mathrmLmathrmT^-1] times [mathrmL] = [mathrmMmathrmL^2mathrmT^-1] ### Pattern Recognition Angular impulse shares the exact same dimensional signature as Planck's constant (h) and angular momentum (L). ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 11 Physics: Units and Measurements Class 11 Physics: System of Particles and Rotational Motion
Q33 jee_main_2024_29_january_evening Error Analysis
A physical quantity Q is found to depend on quantities a, b, c by the relation Q = fraca^4 b^3c^2. The percentage error in a, b and c are 3\%, 4\% and 5\% respectively. Then, the percentage error in Q is:
  • A. 66\%
  • B. 43\%
  • C. 34\%
  • D. 14\%

Solution

### Related Formula For a quantity Q = fraca^x b^yc^z, the maximum relative error is: fracDelta QQ = x fracDelta aa + y fracDelta bb + z fracDelta cc Multiplying by 100 gives the percentage error equation: \%text error in Q = x(\%text error in a) + y(\%text error in b) + z(\%text error in c) ### Core Logic Given formula: Q = fraca^4 b^3c^2 Applying the error propagation rule: fracDelta QQ times 100 = 4 left(fracDelta aa times 100right) + 3 left(fracDelta bb times 100right) + 2 left(fracDelta cc times 100right) ### Step 1: Substitute the Percentage Errors Substitute the given values: * \%text error in a = 3\% * \%text error in b = 4\% * \%text error in c = 5\% \%text error in Q = 4(3\%) + 3(4\%) + 2(5\%) \%text error in Q = 12\% + 12\% + 10\% = 34\% ### Pattern Recognition Error percentages always add up, weighted by their exponents in the mathematical expression, regardless of whether the variable is in the numerator or denominator. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 11 Physics: Units and Measurements
Q38 jee_main_2024_27_jan_morning Measuring Instruments
Identify the physical quantity that cannot be measured using a spherometer:
  • A. textRadius of curvature of concave surface
  • B. textSpecific rotation of liquids
  • C. textThickness of thin plates
  • D. textRadius of curvature of convex surface

Solution

### Core Logic A spherometer is a mechanical instrument designed to measure small vertical displacements to calculate the thickness of thin plates or the radius of curvature of spherical (convex/concave) surfaces. Specific rotation of liquids is an optical property measured via a polarimeter, completely outside the scope of a spherometer. ### Pattern Recognition Spherometers operate purely on linear micrometer screw scale geometry, hence restricted strictly to spatial dimensions. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 11 Physics: Units and Measurements
Q47 jee_main_2024_27_jan_morning Dimensional Analysis
Given below are two statements: Statement (I): Planck's constant and angular momentum have same dimensions. Statement (II): Linear momentum and moment of force have same dimensions. In the light of the above statements, choose the correct answer from the options given below:
  • A. textStatement I is true but Statement II is false
  • B. textBoth Statement I and Statement II are false
  • C. textBoth Statement I and Statement II are true
  • D. textStatement I is false but Statement II is true

Solution

### Core Logic Evaluate dimensions step-by-step: 1. **Planck's constant (h)**: E = h u implies [h] = frac[E][ u] = fractextML^2textT^-2textT^-1 = textML^2textT^-1 2. **Angular momentum (L)**: L = mvr implies [L] = textM cdot textLT^-1 cdot textL = textML^2textT^-1 Since [h] = [L], Statement I is true. 3. **Linear momentum (P)**: P = mv implies [P] = textMLT^-1 4. **Moment of force (Torque tau)**: tau = F r implies [tau] = textMLT^-2 cdot textL = textML^2textT^-2 Since [P] neq [tau], Statement II is false. ### Pattern Recognition Planck's constant can always be paired with angular momentum units (Joule-seconds), while moment of force matches work/energy footprints, not translational momentum. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 11 Physics: Units and Measurements

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