The dimensions of surface tension are
The correct answer and explanation is:
The dimensions of surface tension are [M T⁻²] or equivalently force per unit length.
Explanation:
Surface tension is a physical property that represents the force acting along the surface of a liquid, causing it to behave like a stretched elastic membrane. It arises due to cohesive forces between molecules at the surface of the liquid.
Definition of Surface Tension:
Surface tension (usually denoted by the Greek letter γ or T) is defined as the force acting along the surface per unit length. Mathematically: Surface tension=ForceLength\text{Surface tension} = \frac{\text{Force}}{\text{Length}}
- Force has dimensions of mass × acceleration, or [MLT−2][M L T^{-2}].
- Length has dimension [L][L].
Therefore, the dimensions of surface tension can be written as: [MLT−2][L]=[MT−2]\frac{[M L T^{-2}]}{[L]} = [M T^{-2}]
This means surface tension has the dimensions of mass per time squared.
Physical Interpretation:
- Surface tension is often expressed in units of Newton per meter (N/m) in the SI system.
- A Newton (N) is equivalent to kg⋅m/s2kg \cdot m/s^2, so N/m simplifies to kg/s2kg/s^2, consistent with the dimensional formula above.
- It represents how much force is exerted along each meter of the liquid’s surface to minimize the surface area.
Relation to Other Quantities:
- Surface tension can also be interpreted as energy per unit area. Energy has dimensions [ML2T−2][M L^2 T^{-2}], and area has dimensions [L2][L^2], so energy per unit area also gives [MT−2][M T^{-2}].
- This duality explains why surface tension affects phenomena such as droplet formation, capillary action, and the shape of liquid surfaces.
In summary, the dimensions of surface tension are force per unit length, expressed as [MT−2][M T^{-2}], reflecting its role as a force acting along a line on the liquid’s surface.