Using the product rule of differentiation: $\frac{d}{dx}[u \cdot v] = u' v + u v'$
Here $u = x^2 \implies u' = 2x$
$v = \cos x \implies v' = -\sin x$

Surface tension is caused by intermolecular cohesive forces in the liquid. In the bulk liquid, molecules experience balanced attractive forces in all directions. At the liquid-gas interface, surface molecules experience an unbalanced inward net attraction towards the bulk, creating tension. Thus, increasing the surface area requires work against these cohesive attractive forces. Both (A) and (R) are true, and (R) is the correct explanation of (A).

Froude number ($Fr$) is a dimensionless parameter defined as the square root of the ratio of inertia force to gravity force:

Where $V$ is flow velocity, $g$ is acceleration due to gravity, and $D$ is hydraulic depth. It governs open channel flow regimes (subcritical $Fr \lt 1$, critical $Fr = 1$, supercritical $Fr \gt 1$). Reynolds number is inertia force to viscous force; Mach number is inertia force to elastic force; Euler number is inertia force to pressure force.