Physics Practice – Learn by Doing

✅ Answer: 14%
\[ \frac{\Delta P}{P} = 3\frac{\Delta a}{a} + 2\frac{\Delta b}{b} + \frac{\Delta c}{c} + \frac{\Delta d}{d} \] Substituting values: \[ \frac{\Delta P}{P} = 3(1\%) + 2(2\%) + 3\% + 4\% = 14\%. \] Hence, the percentage error in \(P\) is: \[ \boxed{14\%} \]

✅ Answer: [F L^-1 T²]
Explanation: Force = Mass × Acceleration → M = F·T²/L.

✅ Answer: Angle
Explanation: Radian has a unit (rad) but is dimensionless (ratio of arc/ radius).

✅ Answer: Coefficient of viscosity
Explanation: 1 Pa·s = 1 N·s·m⁻² = viscosity dimension [M L⁻¹ T⁻¹].

✅ Answer: Acceleration due to gravity
Explanation: Spring constant, surface tension, and surface energy are related to force/energy per unit area. g has [L T⁻²], so it is different.

✅ Answer: None of these
Explanation: Pressure gradient = Pressure/Length = [M L⁻² T⁻²]. This does not match velocity gradient, potential gradient, or energy gradient.

✅ Answer: [M L² T⁻³ A⁻²]
Explanation: Ohm’s law: R = V/I. V = Work/Charge = (M L² T⁻²)/(A T) = M L² T⁻³ A⁻¹. Divide by I (A), → M L² T⁻³ A⁻².

✅ Answer: [L T⁻¹]
Explanation: \((\mu₀ε₀)^{-1/2}\) = velocity of light. Dimensions of velocity are [L T⁻¹].

✅ Answer: Time
Explanation: L/R = (Henry / Ohm) = seconds. R·C = (Ohm·Farad) = seconds. Both represent time constants.

✅ Answer: Frequency
Explanation: h has dimensions [M L² T⁻¹]. I has [M L²]. h/I = T⁻¹ = frequency.