[M L T^{-1}] is momentum and [M L^{2} T^{-3}] is power, so option B is correct.

Modulus of elasticity has units of pressure (force per area), so it shares the same dimensions as pressure.

Impulse and momentum both have dimensions of ML T^-1, so option A is correct.

Heat has same dimensions as energy (M L^2 T^-2), none of the provided option strings match that dimension, so 'None of these' is correct.

Mass has units kg while moment of inertia has units kg·m^2, so they do not have identical dimensions; option C is correct.

Velocity^2 has dimensions L^2 T^-2 while radius has dimension L, so they cannot be added; none of the listed physical constants shares such mixed dimensions, so option D is correct.

A dimension describes the qualitative nature or type of a physical quantity (e.g., length, mass), so 'Qualitative' is correct.

Kinetic energy and potential energy are both forms of energy and share the same dimensions, which are [M L^2 T^-2], so option B is correct.

Force, pressure and the gravitational constant each include a T^-2 factor in their dimensional formulas, so all of these have T^-2 present.

Energy density (energy per unit volume) has the same units as pressure (N/m^2), so it represents pressure.