EAPCET UNITS & MEASUREMENT April 13, 2026 by sriumanet@gmail.com Spread the love EAPCET UNITS & MEASUREMENT 1 / 20 If force (F), velocity (v), and time (t) are fundamental quantities, the dimensional formula of mass is: Fvt⁻¹ Ft/v Fv⁻¹t Fvt Force = Mass × Acceleration F = M × (L/T²) ⇒ M = F × T² / L Velocity v = L/T ⇒ L = vT Substitute: M = F × T² / (vT) = Ft / v 2 / 20 The dimensional formula of Planck’s constant divided by energy is: [T] [T⁻¹] [M⁰] [L] E = hv ⇒ h = E / v v (frequency) = T⁻¹ So: h/E = 1/v = T 3 / 20 Which quantity has dimensions same as torque? Energy Power Pressure Momentum Torque = Force × Distance = ML²T⁻² Energy has same dimension 4 / 20 If x = a + bt² + ct³, dimensions of c are: [LT⁻³] [LT⁻²] [LT⁻¹] [L] x = a + bt² + ct³ Each term must have dimension of length ct³ → c = L / T³ 5 / 20 The percentage error in area of square due to error in side is: same double half zero Area = a² % error = 2 × (% error in side) 6 / 20 Dimensional formula of surface tension: [MT⁻²] [ML⁻¹T⁻²] [MLT⁻²] [M⁰LT⁻¹] Surface tension = Force / Length = (MLT⁻²) / L = MT⁻² 7 / 20 Which is NOT possible using dimensional analysis? Verify equation Find constants Derive relation Check homogeneity Dimensional analysis cannot find numerical constants (like 2, π) 8 / 20 If E = hv, dimensions of h are: [ML²T⁻¹] [ML²T⁻²] [MLT⁻¹] [MLT⁻²] E = hv ⇒ h = E / v E = ML²T⁻², v = T⁻¹ So h = ML²T⁻¹ 9 / 20 Relative error in (A/B): ΔA + ΔB ΔA/A + ΔB/B ΔA/A – ΔB/B ΔA/A × ΔB/B For division: Relative error = ΔA/A + ΔB/B 10 / 20 Dimensional formula of coefficient of viscosity: [ML⁻¹T⁻¹] [MLT⁻²] [ML²T⁻²] [M⁰LT⁻¹] Viscosity = (Force × time) / Area = [MLT⁻² × T] / L² = ML⁻¹T⁻¹ 11 / 20 Which quantity has dimension [M⁰L⁰T⁰]? Strain Force Momentum Energy Strain = change/original → ratio → dimensionless 12 / 20 If P = aρgh, dimensions of a are: dimensionless [L] [T] [M] P = aρgh ρgh already has pressure dimension ⇒ a is dimensionless 13 / 20 Dimensional formula of angular velocity: [T⁻¹] [LT⁻¹] [L⁻¹T⁻¹] [M⁰] Angular velocity = angle/time Angle is dimensionless ⇒ T⁻¹ 14 / 20 If velocity v ∝ xᵃ tᵇ, find a and b: 1, -1 0, 1 1, 1 -1, 1 v ∝ xᵃ tᵇ v = LT⁻¹ So: L = Lᵃ ⇒ a = 1 T⁻¹ = Tᵇ ⇒ b = -1 15 / 20 Error in sum of two quantities is: product difference sum of absolute errors ratio 16 / 20 The dimensional formula of Young’s modulus is: [ML⁻¹T⁻²] [MLT⁻²] [ML²T⁻²] [M⁰LT⁻¹] Stress = Force/Area = ML⁻¹T⁻² Young’s modulus = Stress 17 / 20 Significant figures in 3.040 × 10²: 3 4 5 2 18 / 20 Which has maximum precision? Vernier caliper Screw gauge Meter scale Ruler Screw gauge has least count → highest precision 19 / 20 Dimensional formula of power: [ML²T⁻³] [ML²T⁻²] [MLT⁻²] [M⁰LT⁻¹] Power = Work / Time = ML²T⁻² / T = ML²T⁻³ 20 / 20 If force ∝ velocityⁿ, find n dimensionally: 1 2 0 cannot be determined Your score isThe average score is 80% 0% Restart quiz Spread the love
