We need to find the pair of quantities whose dimensions do not include length ([L]). Let's analyze the dimensions of each quantity: - Surface tension Defined as force per unit length. Dimension is [Force]/[Length] = [MLT⁻²]/[L] = [MT⁻²]. It has no length dimension. - Angular momentum Defined as the product of moment of inertia and angular velocity (Iω) or cross product of position and linear momentum (r x p). Dimension is [ML²] [T⁻¹] = [ML²T⁻¹]. It has a length dimension. - Strain Defined as the ratio of change in dimension to the original dimension (e.g., change in length / original length). Dimension is [L]/[L] = [Dimensionless]. It has no length dimension. - Mass density Defined as mass per unit volume. Dimension is [M]/[L³] = [ML⁻³]. It has a length dimension. - Pressure gradient Defined as change in pressure per unit distance. Dimension is [Pressure]/[Length]. Pressure is [Force]/[Area] = [MLT⁻²]/[L²] = [ML⁻²T⁻²]. So, pressure gradient is [ML⁻²T⁻²]/[L] = [ML⁻³T⁻²]. It has a length dimension. - Angle Defined as the ratio of arc length to radius. Dimension is [L]/[L] = [Dimensionless]. It has no length dimension.Now let's check the pairs: A) Surface tension ([MT⁻²]) and angular momentum ([ML²T⁻¹]). Angular momentum has length. B) Surface tension ([MT⁻²]) and strain ([Dimensionless]). Neither has length. C) Angular momentum ([ML²T⁻¹]) and mass density ([ML⁻³]). Both have length. D) Pressure gradient ([ML⁻³T⁻²]) and angle ([Dimensionless]). Pressure gradient has length.The pair with no length dimension is Surface tension and Strain.