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When small object such as needle is put on the surface of water it displaces small amount of water which creates a depression under the object. Such depression increases surface area of the water because of which surface tension tends to decrease it.

Explanation why surface tension balances the weight of an object is that integration of surface tension along the contour or wetted length of the object yields that there is an resultant upward force balancing weight of an object if weight isn't bigger than that resultant. This upward resultant is essentially consequence of curved depression or contour under the object which I already mentioned.

Why is surface tension acting on the object since surface tension is a tendency to decrease surface area of the liquid because of which it should act on the liquid not the object?

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  • $\begingroup$ A simple analogy in 2 dimensions: a weight is suspended on the middle of a rubber band supported between two immovable points. The upward force on the weight is entirely due to the tension on the rubber band, which has an upward vector component when the rubber band is displaced such that it has upward facing curvature. $\endgroup$
    – g s
    Oct 6, 2021 at 19:25

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When a movement Δx would tend to increase the total energy of the system ΔE, Nature tends to respond with a restoring force ΔE/Δx. Here, downward movement of the nonwetted floating object—prompted by gravity—would tend to increase the surface area and thus the surface energy of the water by bending it farther down, so Nature's response is a force acting upward on the object.

(In contrast, without an object, a force arises parallel to the surface if we try to extend the water’s surface area. It all comes down to the direction of the disturbance.)

You can think of the response as being spring-like, as any smooth energy minimum acts like a mechanical spring for small displacements.

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