Among the following quantities, which one has dimension different from the remaining three?

Solution (By Examveda Team)

The question asks us to find the quantity with a different dimension compared to the others. Remember, dimension refers to the fundamental units (like mass, length, and time) that make up a physical quantity.

Let's examine each option:

Option A: Energy per unit volume
Energy has dimensions of [ML²T^-2] and volume has dimensions of [L³]. So, energy per unit volume has dimensions of [ML²T^-2]/[L³] = [ML^-1T^-2].

Option B: Product of voltage and charge per unit volume
Voltage * charge = Energy,so Energy per unit volume and dimension is [ML^-1T^-2]

Option C: Angular momentum per unit mass
Angular momentum is defined as Iω (moment of inertia * angular velocity). So, its dimensions are [ML²T^-1].
Dividing by mass gives: [L²T^-1]

Option D: Force per unit area
Force has dimensions of [MLT^-2] and area has dimensions of [L²]. So, force per unit area has dimensions of [MLT^-2]/[L²] = [ML^-1T^-2].

Notice that Options A,B and D all have dimensions of [ML^-1T^-2]. Option C, however, has dimensions of [L²T^-1].

Therefore, the answer is Option C: Angular momentum per unit mass because its dimensions are different from the other three options.