NEET Dimensions MCQs & PYQs

Energy has the dimensions of work, which is \(\text{Force} \times \text{displacement}\). Since displacement has the dimensions of \(text{acceleration} \times \text{time}^2 = [A][T^2]\), the dimensional formula of energy is \([F][A][T^2]\).

The argument of the logarithm must be dimensionless, so \([b] = [x] = [L]\). Since the logarithm term is dimensionless, \([a] = [F] = [MLT^{-2}]\).

Impulse is given by \(I = F \cdot t = [MLT^{-2}][T] = [MLT^{-1}]\).

In mechanics, we have only three base dimensions (M, L, T). Thus, we cannot determine more than three independent exponents. If two quantities have the same dimensions, they cannot be resolved independently, making R false.

By the principle of homogeneity, only physical quantities with identical dimensions can be added or subtracted. Velocity and velocity gradient have different dimensions, hence they cannot be subtracted.

An angle has a unit (radian) but is dimensionless, so A is false. Any physical quantity that possesses dimensions must have a unit, so R is also false.

The physical magnitude is invariant, expressed as \(n u = \text{constant}\). Therefore, numerical value is inversely proportional to the unit size. A smaller unit leads to a larger numerical value, making R false.

A dimensionally consistent equation is not guaranteed to be physically correct, as dimensionless constants cannot be verified through dimensional analysis. Thus, R is false.

Pressure has dimensions of \([M L^{-1} T^{-2}]\). Energy density (energy per unit volume) also simplifies to \([M L^{-1} T^{-2}]\). Since their dimensions are identical, they share the same SI units.

Base quantities are mutually independent and cannot be defined in terms of each other, making the exponent of one base quantity in another zero. Both statements are true, but R is not the explanation of A.