Units, Measurement & Vectors: 29 MCQs with Explanations

Angular momentum L = r × p, where r has dimension [L] and p (linear momentum) has dimension [M L T^-1]. Therefore, L = [L] × [M L T^-1] = [M L^2 T^-1].

Coefficient of viscosity η has SI unit Ns/m² or Pa·s (Pascal-second).

Electric flux Φ = E·A has units N/C × m² = Nm²/C. Since 1 N/C = 1 V/m, units also = Vm.

Planck's constant h has dimensions [M L² T⁻¹], same as angular momentum.

Magnetic flux Φ has SI unit Weber (Wb). 1 Wb = 1 T·m².

The SI base unit of electric current is the ampere (A), defined as the constant current that would produce a force of 2×10⁻⁷ newtons per meter of length between two parallel conductors placed 1 meter apart in vacuum.

Force = mass × acceleration. Mass has dimension [M], acceleration has dimension [LT⁻²]. Therefore, force has dimensional formula [M][LT⁻²] = [MLT⁻²].

Power is the rate of doing work. SI unit of power is watt (W), where 1 W = 1 J/s.

Magnetic flux Φ = B·A (for uniform field perpendicular to area). SI unit is weber (Wb), where 1 Wb = 1 T·m².

Poisson's ratio σ = (lateral strain)/(longitudinal strain). It is dimensionless and typically between 0 and 0.5 for most materials.

Gravitational field strength g = F/m has units N/kg, which is dimensionally equivalent to m/s² (acceleration).

SI unit is becquerel (Bq = 1 decay/s). Traditional unit is curie (Ci = 3.7 × 10¹⁰ Bq). Both are units of radioactivity (decay rate).

From Stokes' law: F = 6πηrv. η = F/(6πrv). Dimensions: [η] = [MLT⁻²]/([L][LT⁻¹]) = [ML⁻¹T⁻¹].

SI unit of inductance is henry (H). 1 H = 1 Wb/A = 1 V·s/A.

Angular momentum L = mvr. Dimensions: [M][LT⁻¹][L] = [ML²T⁻¹].

SI unit of electric charge is coulomb (C). 1 C = 1 A·s.

Electric charge is measured in coulombs (C). One coulomb is the charge transported by a constant current of one ampere in one second (1 C = 1 A·s).

Planck's constant h has dimensions [M L² T⁻¹], same as angular momentum (L = r × p).

Magnetic flux Φ has SI unit Weber (Wb). 1 Wb = 1 T·m². Tesla is unit of magnetic field; Gauss is CGS unit of magnetic field.

From F = Gm₁m₂/r², G = Fr²/m₁m₂. Dimensions: [M L T^-2][L²]/[M²] = [M^-1 L^3 T^-2].

Becquerel (Bq) = 1 disintegration per second. Curie (Ci) = 3.7 × 10¹⁰ Bq (activity of 1g radium).

Capacitance C has SI unit Farad (F). 1 F = 1 C/V.

The prefix 'nano' represents 10⁻⁹. Therefore, 1 nanosecond = 10⁻⁹ seconds.

Force = mass × acceleration. Acceleration has dimensions of [LT⁻²]. Therefore, Force has dimensions of [M] × [LT⁻²] = [MLT⁻²].

The tesla is the SI unit of magnetic flux density (B). It is defined as one weber per square meter (Wb/m²). It can also be expressed as 1 N/(A·m).

Electric field intensity (E) is defined as force per unit charge (N/C). It is also defined as the potential gradient (V/m). Both N/C and V/m are equivalent SI units for the electric field.

Resistivity (ρ) is an intrinsic property of the material. It depends on the nature of the material and temperature, but not on the dimensions (length or cross-sectional area) of the wire. Therefore, it remains ρ.

The decay constant λ represents the probability per unit time that a nucleus will decay. From the decay law N = N₀e⁻λt, the exponent must be dimensionless. Therefore, λ must have units of 1/time, such as s⁻¹.

Planck's constant has units of energy × time (J·s). Energy has dimensions [ML²T⁻²]. Multiplying by time [T] gives [ML²T⁻¹].