question_answer

A thin metal disc of radius r floats on water surface and bends the surface downwards along the perimeter making an angle q with vertical edge of the disc. If the disc displaces a weight of water W and surface tension of water is T, then the weight of metal disc is                                  [AMU (Med.) 1999]

A)             \[2\pi rT+W\] 

B)             \[2\pi rT\cos \theta -W\]

C)             \[\text{2}\pi \text{rTcos}\theta +W\]

D)             \[W-2\pi rT\cos \theta \]

Correct Answer: C

Solution :

            Weight of metal disc = total upward force = upthrust force + force due to surface tension = weight of displaced water \[+Tcos\theta (2\pi r)\]             \[=W+2\pi rTcos\theta \]