For the determination of refractive index of glass slab, a travelling microscope is used whose main scale contains 300 equal divisions equals to 15 cm. The vernier scale attached to the microscope has 25 divisions equals to 24 divisions of main scale. The least count (LC) of the travelling microscope is (in cm):

### Related Formula Resistivity formula: rho = RfracAl = Rfracpi r^2l$$\rho = R\frac{A}{l} = R\frac{\pi r^2}{l}$$ Maximum relative error equation: fracDeltarhorho = fracDelta RR + 2fracDelta rr + fracDelta ll$$\frac{\Delta\rho}{\rho} = \frac{\Delta R}{R} + 2\frac{\Delta r}{r} + \frac{\Delta l}{l}$$ ### Core Logic Substitute the measured fractions: fracDeltarhorho = frac10100 + 2left(frac0.050.35right) + frac0.215$$\frac{\Delta\rho}{\rho} = \frac{10}{100} + 2\left(\frac{0.05}{0.35}\right) + \frac{0.2}{15}$$ fracDeltarhorho = frac110 + 2left(frac17right) + frac175$$\frac{\Delta\rho}{\rho} = \frac{1}{10} + 2\left(\frac{1}{7}\right) + \frac{1}{75}$$ fracDeltarhorho = 0.1 + 0.2857 + 0.0133 = 0.399$$\frac{\Delta\rho}{\rho} = 0.1 + 0.2857 + 0.0133 = 0.399$$ ### Step 1: Convert to Percentage \% severance = 0.399 times 100\% = 39.9\%$$\% severance = 0.399 \times 100\% = 39.9\%$$ ### Pattern Recognition The power of 2 in r^2$r^2$ 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

### Related Formula Angular Impulse equation: textAngular Impulse = int tau \, dt = Delta L$$\text{Angular Impulse} = \int \tau \, dt = \Delta L$$ textAngular Momentum (L) = mvr$$\text{Angular Momentum } (L) = mvr$$ ### Core Logic By the impulse-momentum theorem for rotation, angular impulse equals the net change in angular momentum. Extract dimensions from [mvr]$[mvr]$: [m] = [mathrmM]$$[m] = [\mathrm{M}]$$ [v] = [mathrmLmathrmT^-1]$$[v] = [\mathrm{L}\mathrm{T}^{-1}]$$ [r] = [mathrmL]$$[r] = [\mathrm{L}]$$ ### Step 1: Combine Dimensions [textAngular Impulse] = [mathrmM] times [mathrmLmathrmT^-1] times [mathrmL] = [mathrmMmathrmL^2mathrmT^-1]$$[\text{Angular Impulse}] = [\mathrm{M}] \times [\mathrm{L}\mathrm{T}^{-1}] \times [\mathrm{L}] = [\mathrm{M}\mathrm{L}^2\mathrm{T}^{-1}]$$ ### Pattern Recognition Angular impulse shares the exact same dimensional signature as Planck's constant (h$h$) and angular momentum (L$L$). ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 11 Physics: Units and Measurements Class 11 Physics: System of Particles and Rotational Motion

### Related Formula For a quantity Q = fraca^x b^yc^z$Q = \frac{a^x b^y}{c^z}$, the maximum relative error is: fracDelta QQ = x fracDelta aa + y fracDelta bb + z fracDelta cc$$\frac{\Delta Q}{Q} = x \frac{\Delta a}{a} + y \frac{\Delta b}{b} + z \frac{\Delta c}{c}$$ Multiplying by 100$100$ gives the percentage error equation: \%text error in Q = x(\%text error in a) + y(\%text error in b) + z(\%text error in c)$$\%\text{ error in } Q = x(\%\text{ error in } a) + y(\%\text{ error in } b) + z(\%\text{ error in } c)$$ ### Core Logic Given formula: Q = fraca^4 b^3c^2$$Q = \frac{a^4 b^3}{c^2}$$ 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)$$\frac{\Delta Q}{Q} \times 100 = 4 \left(\frac{\Delta a}{a} \times 100\right) + 3 \left(\frac{\Delta b}{b} \times 100\right) + 2 \left(\frac{\Delta c}{c} \times 100\right)$$ ### Step 1: Substitute the Percentage Errors Substitute the given values: * \%text error in a = 3\%$\%\text{ error in } a = 3\%$ * \%text error in b = 4\%$\%\text{ error in } b = 4\%$ * \%text error in c = 5\%$\%\text{ error in } c = 5\%$ \%text error in Q = 4(3\%) + 3(4\%) + 2(5\%)$$\%\text{ error in } Q = 4(3\%) + 3(4\%) + 2(5\%)$$ \%text error in Q = 12\% + 12\% + 10\% = 34\%$$\%\text{ error in } Q = 12\% + 12\% + 10\% = 34\%$$ ### 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

### 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

### Core Logic Evaluate dimensions step-by-step: 1. **Planck's constant (h$h$)**: E = h u implies [h] = frac[E][ u] = fractextML^2textT^-2textT^-1 = textML^2textT^-1$$E = h u \implies [h] = \frac{[E]}{[ u]} = \frac{\text{ML}^2\text{T}^{-2}}{\text{T}^{-1}} = \text{ML}^2\text{T}^{-1}$$ 2. **Angular momentum (L$L$)**: L = mvr implies [L] = textM cdot textLT^-1 cdot textL = textML^2textT^-1$$L = mvr \implies [L] = \text{M} \cdot \text{LT}^{-1} \cdot \text{L} = \text{ML}^2\text{T}^{-1}$$ Since [h] = [L]$[h] = [L]$, Statement I is true. 3. **Linear momentum (P$P$)**: P = mv implies [P] = textMLT^-1$$P = mv \implies [P] = \text{MLT}^{-1}$$ 4. **Moment of force (Torque tau$\tau$)**: tau = F r implies [tau] = textMLT^-2 cdot textL = textML^2textT^-2$$\tau = F r \implies [\tau] = \text{MLT}^{-2} \cdot \text{L} = \text{ML}^2\text{T}^{-2}$$ Since [P] neq [tau]$[P] \neq [\tau]$, 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