Question

A light metal disc of radius ‘r’ floats on water surface and bends the surface downwards along the perimeter making an angle ‘θ’ with the vertical edge of the disc. If the weight of water displaced by the disc is ‘W’, the weight of the metal disc is ______.

[T = surface tension of water]

Options

• W − 2πT cosθ

• 2πT + W

• 2πT cosθ + W

• 2πT cosθ − W

Answer 1

A light metal disc of radius ‘r’ floats on water surface and bends the surface downwards along the perimeter making an angle ‘θ’ with the vertical edge of the disc. If the weight of water displaced by the disc is ‘W’, the weight of the metal disc is 2πT cosθ + W.

Explanation:

The weight of the disc is balanced by the force due to the surface tension and the upthrust of water. After resolving surface tension into its components, it could be seen that the component of surface tension in the vertically upward direction is Tcosθ, and the force acting due to it is 2πT cosθ. The upthurst is equal to the weight of the water displaced (W).

∴ Weight of the disc = 2πT cosθ + W