What is the difference between an ordinary stretched elastic membrane and that of the free surface of liquid?

Ordinary stretched elastic membrane obeys Hooke’s law i.e., tension increases with stretching while tension in the liquid does not increase on increasing the area. When the elastic membrane is stretched, the separation between the molecules increases.

In case of liquid when surface area is increased the molecules move from bulk to surface film and the distance between the molecules remains constant. 
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Why a piece of camphor placed on the surface of water begins to dance?

When impurities are dissolved in water, surface tension of water decreases. Hence, when camphor is dissolved in water, surface tension will decrease. Camphor being non-symmetrical, different amount of camphor is dissolved from different sides. Therefore, Surface tension will be different on different sides. Hence, unbalanced force sets the piece into motion and the piece of camphor begins to dance. 
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Why small mercury drops are spherical but large ones are flat?

A drop of mercury tries to acquire the minimum surface area due to surface area, for any given volume minimum area is for sphere. The effect of gravity is less for small droplets, hence the mercury drops are nearly spherical in shape. 

As  the size of drop increases, force of gravity on the drop increases which tries to deform the shape. Therefore, bigger drops are flat.
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Why are rain drops spherical?

For any given volume, the sphere acquires a minimum surface area. Rain drops fall freely under the effect of gravity and is in a state of weightlessness. The only force on them is surface tension due to which the drops have tendency to acquire a minimum surface area. Therefore, the rain drops acquire spherical shapes.
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Why the nib of a pen is split?


The tip of nib of a writing pen is split to provide the capillary action.
Due to capillarity, ink will rise in the split of nib and allows the pen to write continuously. 
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