Consider a modified Bernoulli equation. left(mathrmP+fracmathrmAmathrmBt^2right)+rhomathrmg(mathrmh+mathrmBt)+frac12rhomathrmV^2=textconstant If t has the dimension of time then the dimensions of A and B are ____, ____ respectively.

Solution & Explanation

### Related Formula textPrinciple of Homogeneity: Only quantities with same dimensions can be added/subtracted. ### Core Logic From the term (h + Bt), h (height/length) and Bt must have the same dimension. [h] = [Bt] [B] = frac[h][t] = frac[L][T] = [L T^-1] So, B = [M^0 L T^-1]. ### Step 1: Finding Dimension of A From the term left(P + fracABt^2right), pressure P and fracABt^2 must have the same dimension. Dimension of Pressure P = fractextForcetextArea = [M L^-1 T^-2]. [P] = left[fracABt^2right] [M L^-1 T^-2] = frac[A][L T^-1] times [T^2] [M L^-1 T^-2] = frac[A][L T] [A] = [M L^-1 T^-2] times [L T] = [M L^0 T^-1] So, A = [M L^0 T^-1]. ### Pattern Recognition Apply the Principle of Homogeneity across any (X + Y) terms inside brackets. Extract one unknown, plug it into the next additive bracket group. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 11 Physics: Units and Measurements Class 11 Physics: Mechanical Properties of Fluids

Reference Study Guides

Units And Measurements

More Units and Measurements Previous-Year Questions — Page 5

Q22 jee_main_2025_24_jan_morning Screw Gauge and Least Count
The least count of a screw guage is 0.01 mathrm~mm . If the pitch is increased by 75 \% and number of divisions on the circular scale is reduced by 50 \% , the new least count will be \_ times 10^-3 mathrm~mm .
Numerical Answer. Answer: 35 to 35

Solution

### Related Formula The Least Count (LC) of a screw gauge tool is defined by: textL.C. = fractextPitchtextTotal Number of Circular Divisions (N) ### Core Logic The initial least count is given as [cite: 167, 788]: textL.C.textinitial = fracPN = 0.01text mm Now, calculate the modified parameters from the text details : * New Pitch: P' = P(1 + 0.75) = 1.75P * New Divisions: N' = N(1 - 0.50) = 0.5N ### Step 1: Calculating the New Least Count Set up the updated least count expression ratio : textL.C.textnew = fracP'N' = frac1.75P0.5N = 3.5 times left(fracPN ight) Substitute the initial least count value : textL.C.textnew = 3.5 times 0.01text mm = 0.035text mm Converting into the requested scientific prefix units (10^-3text mm) : textL.C.textnew = 35 times 10^-3text mm Therefore, the requested value is 35. ### Pattern Recognition Least count scales proportionally with pitch increases, and inversely with reductions in circular divisions. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 11 Physics: Units and Measurements
Q3 jee_main_2025_28_jan_evening Dimensional Analysis
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:
  • A. text(A)-(III), (B)-(I), (C)-(IV), (D)-(II)
  • B. text(A)-(I), (B)-(III), (C)-(IV), (D)-(II)
  • C. text(A)-(III), (B)-(I), (C)-(II), (D)-(IV)
  • D. text(A)-(II), (B)-(I), (C)-(IV), (D)-(III)

Solution

### 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
Q jee_main_2025_29_jan_morning Dimensional Analysis
The pair of physical quantities not having same dimensions is :
  • A. textTorque and energy
  • B. textSurface tension and impulse
  • C. textAngular momentum and Planck\'s constant
  • D. textPressure and Young\'s modulus

Solution

### Core Logic Let\'s check the dimensions of each pair : * textTorque = [textEnergy] = [ML^2T^-2] * textSurface Tension = [MT^-2] vs textImpulse = [MLT^-1] * [textAngular Momentum] = [textPlanck\'s Constant] = [ML^2T^-1] * [textPressure] = [textYoung\'s Modulus] = [ML^-1T^-2] ### Step 1: Identify Non-Matching Pair Surface tension and impulse do not share matching dimension frameworks. ### Pattern Recognition Surface tension is force per unit length ([MT^-2]), while impulse is force times time ([MLT^-1]) ### Chapter Mix Class 11 Physics: Units and Measurements
Q jee_main_2025_29_jan_morning Dimensional Homogeneity
The expression given below shows the variation of velocity (v) with time (t), v = At^2 + fracBtC + t . The dimension of ABC is:
  • A. left[mathrmM^0 mathrm~L^2 mathrmT^-3right]
  • B. left[mathrmM^0 mathrm~L^1 mathrmT^-3right]
  • C. [mathrmM^0mathrmL^1mathrmT^-2]
  • D. left[mathrmM^0 mathrm~L^2 mathrmT^-2right]

Solution

### Related Formula [v] = [At^2] = left[fracBtC+tright] ### Core Logic By the principle of dimensional homogeneity: 1. [C] = [t] = [T] 2. [At^2] = [v] implies [A][T^2] = [LT^-1] implies [A] = [LT^-3] 3. left[fracBtTright] = [v] implies [B] = [LT^-1] ### Step 1: Calculate Dimensions of ABC [ABC] = [LT^-3] cdot [LT^-1] cdot [T] = [L^2 T^-3] ### Pattern Recognition Denominator terms matched first give C, tracking linear velocity units sets the balance for A and B ### Chapter Mix Class 11 Physics: Units and Measurements
Q42 jee_main_2024_01_february_morning Vernier Calliper
10 divisions on the main scale of a Vernier calliper coincide with 11 divisions on the Vernier scale. If each division on the main scale is of 5 units, the least count of the instrument is:
  • A. frac12
  • B. frac1011
  • C. frac5011
  • D. frac511

Solution

### Related Formula Least Count (LC) definition: textLC = 1text MSD - 1text VSD ### Core Logic From the problem: 10text MSD = 11text VSD implies 1text VSD = frac1011text MSD Substitute into the Least Count formula: textLC = 1text MSD - frac1011text MSD = frac111text MSD ### Step 1: Calculate with Main Scale Units Given that 1text MSD = 5text units: textLC = frac111 times 5 = frac511text units ### Pattern Recognition Watch out for unconventional scale arrangements where textVSD > textMSD. The fundamental difference formula 1text MSD - 1text VSD safely determines magnitudes without needing sign corrections. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 11 Physics: Units and Measurements

More Units and Measurements Questions — jee_main_2026_21_jan_morning

Practice all Units and Measurements previous-year questions →

Rankbit System
JEE Physics: Waves (+15.5%) | Electrostatics: Concentric Shells (-29.7%) | Modern Physics: Photoelectric Clones (+34.2%) | Mathematics: Definite Integrals (+18.1%) | Chemistry: Coordination Splitting (-11.4%) | JEE Physics: Waves (+15.5%) | Electrostatics: Concentric Shells (-29.7%) | Modern Physics: Photoelectric Clones (+34.2%) | Mathematics: Definite Integrals (+18.1%) | Chemistry: Coordination Splitting (-11.4%)
YOUR FIRST PREP STEP STARTS HERE

We Map Every Repeating Question in Competitive Exams.

Say goodbye to generic mock test fatigue. RankBit uses smart analysis to group past exam questions into their foundational Repeating Question Types. Find chapter weightage, track repeating questions, and score higher with targeted practice.

Select Your Target Exam

Choose an exam track below to find formulas per chapter and patterns.

Syncing Exam Intelligence

Mapping formulas and patterns across all tracks…

PATH A — FULL LENGTH PRACTICE

Full Mock Test Hub

Simulate real NTA exam conditions with fully tracked mocks. Time yourself against past papers.

Now Live Open
PATH B — TARGETED PRACTICE

Topic-wise Practice Hub

Practice past-year questions one chapter at a time. Pick an exam → subject → chapter and get every PYQ for that topic — pulled together from all past papers — with the chapter's key formulas alongside.

Loading Questions... Browse Topics

Exam Analysis Tools

Chapter weightage trends and topic-wise practice — all mapped from past shift papers.

Year-wise PYQ

Chapter Weightage & Trends

See high-yield chapters, year-wise counts and the frequency-based chance each topic repeats next exam.

Weightage Board Open
Targeted PYQs

Topic-wise Practice Hub

Every past-year question for a chapter pulled from all papers, with its key formulas alongside.

One chapter at a time Open
Latest from the Blog
View all →

Loading articles...