### Related Formula Ratio formulation: fracphi_Ephi_M = fracE cdot AB cdot A = fracEB $ \frac{\phi_E}{\phi_M} = \frac{E \cdot A}{B \cdot A} = \frac{E}{B} $ From Maxwell's electromagnetic wave equations: E = c cdot B implies fracEB = c$ E = c \cdot B implies \frac{E}{B} = c$ where c$c$ is the speed of light. ### Core Logic Since the ratio reduces to the dimension of speed (c$c$): left[fracphi_Ephi_M ight] = [c] = mathrmM^0 mathrmL^1 mathrmT^-1 mathrmA^0$\left[\frac{\phi_E}{\phi_M} ight] = [c] = \mathrm{M}^0 \mathrm{L}^1 \mathrm{T}^{-1} \mathrm{A}^0$ ### Step 1: Identify Exponent Values Matching indices with mathrmM^PmathrmL^QmathrmT^RmathrmA^S$\mathrm{M}^{P}\mathrm{L}^{Q}\mathrm{T}^{R}\mathrm{A}^{S}$: * P = 0$P = 0$ * Q = 1$Q = 1$ * R = -1$R = -1$ * S = 0$S = 0$ Hence, (Q, R) = (1, -1)$(Q, R) = (1, -1)$. ### Pattern Recognition Flux areas cancel out immediately. The ratio fracEB$\frac{E}{B}$ always carries the dimension of velocity (LT^-1$LT^{-1}$). ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 11 Physics: Units and Measurements Class 12 Physics: Electromagnetic Waves

### Core Logic Let's derive the dimensional formulas systematically: * **(A) Mass density:** rho = fractextMasstextVolume = fracML^3 = [M^1 L^-3 T^0] implies text(IV)$\rho = \frac{\text{Mass}}{\text{Volume}} = \frac{M}{L^3} = [M^1 L^{-3} T^0] \implies \text{(IV)}$ [cite: 765]. * **(B) Impulse:** I = F cdot Delta t = [M^1 L^1 T^-2] cdot [T] = [M^1 L^1 T^-1] implies text(II)$I = F \cdot \Delta t = [M^1 L^1 T^{-2}] \cdot [T] = [M^1 L^1 T^{-1}] \implies \text{(II)}$ [cite: 767]. * **(C) Power:** P = fractextWorktextTime = frac[M^1 L^2 T^-2][T] = [M^1 L^2 T^-3] implies text(I)$P = \frac{\text{Work}}{\text{Time}} = \frac{[M^1 L^2 T^{-2}]}{[T]} = [M^1 L^2 T^{-3}] \implies \text{(I)}$ [cite: 770]. * **(D) Moment of inertia:** I = M r^2 = [M^1 L^2 T^0] implies text(III)$I = M r^2 = [M^1 L^2 T^0] \implies \text{(III)}$ [cite: 772]. Matching all four pairings establishes the layout: (A)-(IV), (B)-(II), (C)-(I), (D)-(III)[cite: 110, 758]. ### Pattern Recognition Isolating the unique matching option for a straightforward parameter like Mass Density (A-IV) or Moment of Inertia (D-III) easily allows exclusion of multiple invalid answer branches instantly[cite: 765, 772]. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 11 Physics: Units and Measurements

### Related Formula In multiplication and division arithmetic rules, the final product or quotient must be rounded off to retain as many significant figures as are present in the least precise operand. ### Core Logic Let us check the significant digit count of the operands in the expression : * 32.3$32.3$ has 3$3$ significant figures. * 1125$1125$ has 4$4$ significant figures. * 27.4$27.4$ has 3$3$ significant figures. The minimum number of significant figures among the numbers is 3$3$. ### Step 1: Rounding Off Direct calculation yield : y = 1326.186...$y = 1326.186...$ Rounding this value off to contain exactly 3 significant figures means changing it to 1330, since the digit after 2 is 6 (which is greater than 5), updating the hundreds spot upwards. ### Pattern Recognition Never keep unearned precision from automated calculation. The output is bounded strictly by your least precise entry. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 11 Physics: Units and Measurements

### Related Formula The Least Count (LC) of a screw gauge tool is defined by: textL.C. = fractextPitchtextTotal Number of Circular Divisions (N) $\text{L.C.} = \frac{\text{Pitch}}{\text{Total Number of Circular Divisions (N)}} $ ### Core Logic The initial least count is given as [cite: 167, 788]: textL.C.textinitial = fracPN = 0.01text mm$\text{L.C.}{\text{initial}} = \frac{P}{N} = 0.01\text{ mm}$ Now, calculate the modified parameters from the text details : * New Pitch: P' = P(1 + 0.75) = 1.75P$P' = P(1 + 0.75) = 1.75P$ * New Divisions: N' = N(1 - 0.50) = 0.5N$N' = N(1 - 0.50) = 0.5N$ ### 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)$\text{L.C.}{\text{new}} = \frac{P'}{N'} = \frac{1.75P}{0.5N} = 3.5 \times \left(\frac{P}{N} ight)$ Substitute the initial least count value : textL.C.textnew = 3.5 times 0.01text mm = 0.035text mm$\text{L.C.}{\text{new}} = 3.5 \times 0.01\text{ mm} = 0.035\text{ mm}$ Converting into the requested scientific prefix units (10^-3text mm$10^{-3}\text{ mm}$) : textL.C.textnew = 35 times 10^-3text mm$\text{L.C.}{\text{new}} = 35 \times 10^{-3}\text{ mm}$ 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

### Related Formula * **Angular Impulse** = Change in Angular Momentum = tau cdot Delta t = [M L^2 T^-2] cdot [T] = [M L^2 T^-1]$\tau \cdot \Delta t = [M L^2 T^{-2}] \cdot [T] = [M L^2 T^{-1}]$ [cite: 670, 672] * **Latent Heat** (L$L$) = fracQm = frac[M L^2 T^-2][M] = [M^0 L^2 T^-2]$\frac{Q}{m} = \frac{[M L^2 T^{-2}]}{[M]} = [M^0 L^2 T^{-2}]$ * **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]$\frac{R \cdot A}{l} = \frac{[M L^2 T^{-3} A^{-2}] \cdot [L^2]}{[L]} = [M L^3 T^{-3} A^{-2}]$ * **Electromotive force** (V$V$) = fracWq = frac[M L^2 T^-2][A T] = [M L^2 T^-3 A^-1]$\frac{W}{q} = \frac{[M L^2 T^{-2}]}{[A T]} = [M L^2 T^{-3} A^{-1}]$ ### 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$L = Q/m$) often immediately eliminates three incorrect options, securing a quick correct answer. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 11 Physics: Units and Measurements