Test: Dimensions of Physical Quantities (NCERT) - NEET MCQ

Among the given physical quantities angle has a unit but no dimensions. Angle = [M°L°T°]
The SI unit of angle is radian.

Relative density is the ratio of two like quantities.
Therefore, it has neither unit nor dimensions.

A dimensionless quantity need not always have a unit, example: angular displacement, θ is dimensionless but has a unit of radians, and quantities like co-efficient of friction, have no dimensions and no units.

we know, force = mass × acceleration
energy = Workdone = force × displacement
power = energy/time
torque = force × perpendicular distance between force and axis of rotation. now, by these formula, find dimension of all terms.
Example: dimension of force = [MLT⁻²]
dimension of energy = [ML²T⁻²]
dimension of power = [ML²T⁻³]
dimension of torque = [ML²T⁻²]
Here it is clear that dimension of energy and dimension of torque are equal.
Hence, option (b) is correct.

Physical quantities having different dimensions cannot be added or subtracted.
As P, Q and R are physical quantities having different dimensions, therefore they can neither be added nor be subtracted.
Thus, (a) can never be a meaningful quantity.