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Given below are two statements: Statement (I): The dimensions of Planck's constant and angular momentum are same. Statement (II): In Bohr's model electron revolve around the nucleus only in those orbits for which angular momentum is integral multiple of Planck's constant. In the light of the above statements, choose the most appropriate answer from the options given below:

Solution & Explanation

### Related Formula E = hf implies [h] = frac[E][f] = fractextMtextL^2textT^-2textT^-1 = textMtextL^2textT^-1 L = mvr implies [L] = textM cdot (textLtextT^-1) cdot textL = textMtextL^2textT^-1 L = fracnh2pi ### Core Logic Statement I: Comparing the dimensional formula of Planck's constant (h) and angular momentum (L), both are identical [textMtextL^2textT^-1]. Hence, Statement I is correct. Statement II: According to Bohr's second postulate, angular momentum is an integral multiple of frach2pi, not an integral multiple of h. Hence, Statement II is incorrect. ### Pattern Recognition Watch out for exact definitions in standard postulates. Bohr's model requires angular momentum to be quantized in units of hbar = frach2pi, making statement II a classic trap. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 11 Physics: Units and Measurements Class 12 Physics: Atoms

Reference Study Guides

Units And Measurements

More Units and Measurements Previous-Year Questions — Page 5

Q4 2025 Dimensional Analysis
The pair of physical quantities not having same dimensions is : [cite: 1, 5]
  • 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])[cite: 5, 630]. ### Chapter Mix Class 11 Physics: Units and Measurements
Q6 2025 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: [cite: 1, 5]
  • 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] [cite: 597, 598] 3. left[fracBtTright] = [v] implies [B] = [LT^-1] [cite: 597, 599] ### 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[cite: 597, 598]. ### Chapter Mix Class 11 Physics: Units and Measurements

More Units and Measurements Questions — jee_main_2025_04_april_evening

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