NEET Physics: dimensional analysis Practice Questions

Correct answer: A — Checking the dimensional correctness of an equation

The principle of homogeneity states that in an equation, the dimensions of all terms on both sides must be the same. This is used to check dimensional consistency.

Correct answer: A — M L² T⁻²

Work (Energy) is defined as Force times distance (W = Fd). Since Force (F=ma) has dimensions MLT⁻² and distance (L) has dimension L, the dimensions of work are (MLT⁻²) × L = ML²T⁻².

Correct answer: A — [M L⁻³]

The dimensional formula for density is mass divided by volume (ρ= m/V). The dimensions are [M] / [L³] = [M L⁻³].

Correct answer: A — Mass times velocity

Momentum (p) is defined as mass times velocity (p = mv). Its dimensions are [MLT⁻¹]. Option B, Mass times velocity, directly corresponds to the definition of momentum and thus has the same dimensions.

Correct answer: C — Correct, because L/T² matches the required dimensions.

Acceleration is defined as change in velocity over time (Velocity/Time), thus its dimensions are [LT⁻¹] / [T] = [LT⁻²]. This confirms dimensional consistency.

Correct answer: D — Magnetic field (H)

Magnetic flux density (B) is often used interchangeably with Magnetic field strength (H) in some contexts or derived from B⃗ = μH⃗. However, dimensionally, Magnetic Flux Density (B) is equivalent to Magnetic Field Strength (H) in terms of [M T⁻² I⁻¹] or [M L T⁻² I⁻¹], which is dimensionally equivalent to the magnetic field intensity (H) in SI units, making A the most conceptually linked dimensionally. (Note: In strict SI dimensional analysis, B and H are often treated as having the same dimensions when considering the field relationship.)

Correct answer: A — Energy

The dimensions [M¹L²T⁻²] correspond to the dimensions of Force (or Work/Energy, which have the same dimensions). Force is MLT⁻².

Correct answer: C — [M L T⁻¹]

Momentum (p) is defined as mass times velocity (p = mv). The dimensions are [M] × [L T⁻¹], which gives [M L T⁻¹].

Correct answer: A — ML²T⁻¹

Angular momentum (L) is defined as the product of the moment of inertia (I, dimension ML²) and angular velocity (ω, dimension T⁻¹). Therefore, the dimension is (ML²) × (T⁻¹) = ML²T⁻¹.

Correct answer: A — ML²T⁻²

Force (F) is defined as mass (M) times acceleration (L/T²). Therefore, the dimensions are M * (L/T²) = MLT⁻².

Correct answer: D — [M L² T⁻²]

Energy (Work) is defined as Force times Distance (W = F · d). Since Force is M L T⁻² and Distance is L, the dimension of Energy is (M L T⁻²) × L = [M L² T⁻²]. This corresponds to Option C.

Correct answer: D — M L T

The fundamental dimensions of any physical quantity are Mass (M), Length (L), and Time (T). Thus, the dimensions of mass are M, length are L, and time are T.

Correct answer: C — ML⁻¹T⁻²

Density is mass divided by volume. The dimensions are [M] / [L³] = ML⁻³T⁻².