At what respective value of a, b, and c would the unit of work, the joule, be dimensionally similar to Ma Lb Tc?

Analyze the question: We need the dimensions of work (joule) written in the form M^a L^b T^c, where M is mass, L is length and T is time.

Concept: Work = Force × Distance, and Force = mass × acceleration (F = ma).

Solution:

1. Dimension of acceleration = L T⁻²
2. Dimension of force = M L T⁻²
3. Dimension of work = Force × Distance = (M L T⁻²) × L = M L² T⁻²

Comparing with M^a L^b T^c:

• a = 1
• b = 2
• c = –2

Check with units: 1 joule = 1 N·m = 1 kg·m/s² × m = kg·m²·s⁻². This matches.

Answer: The values are 1, 2, –2, which is option B.

Tip: Remember that energy and work share the same dimensions, M L² T⁻². Kinetic energy ½mv² gives M (L T⁻¹)² = M L² T⁻², so you can check any energy-related formula this way. Option C (1, 1, –2) is the trap. It is the dimension of force (newton), not work.