Explain why:
$(a)$ The angle of contact of mercury with glass is obtuse,while that of water with glass is acute.
$(b)$ Water on a clean glass surface tends to spread out while mercury on the same surface tends to form drops. (Put differently,water wets glass while mercury does not.)
$(c)$ Surface tension of a liquid is independent of the area of the surface.
$(d)$ Water with detergent dissolved in it should have small angles of contact.
$(e)$ $A$ drop of liquid under no external forces is always spherical in shape.

(N/A) The angle between the tangent to the liquid surface at the point of contact and the solid surface inside the liquid is called the angle of contact $(\theta)$,as shown in the figure.
$S_{la}$,$S_{sa}$,and $S_{sl}$ are the respective interfacial tensions between the liquid-air,solid-air,and solid-liquid interfaces. At the line of contact,the surface forces between the three media must be in equilibrium,i.e.,
$\cos \theta = \frac{S_{sa} - S_{sl}}{S_{la}}$
$(a)$ Mercury molecules have a strong cohesive force (attraction between themselves) and a weak adhesive force (attraction toward glass). Thus,$S_{sl} > S_{sa}$,making $\cos \theta$ negative,which results in an obtuse angle of contact.
$(b)$ Water molecules have a weak cohesive force and a strong adhesive force toward glass. Thus,$S_{sa} > S_{sl}$,making $\cos \theta$ positive,which results in an acute angle of contact. Consequently,water spreads to maximize contact area,while mercury forms drops to minimize it.
$(c)$ Surface tension is defined as the force acting per unit length at the interface. It is a property of the liquid-surface interface and is independent of the total surface area.
$(d)$ Detergents reduce the surface tension of water. $A$ smaller angle of contact $(\theta)$ facilitates better wetting and capillary action,allowing the detergent solution to penetrate deep into fabrics.
$(e)$ Due to surface tension,a liquid tends to minimize its surface area. For a given volume,a sphere has the minimum surface area. Therefore,in the absence of external forces,liquid drops are spherical.