Question

A mosquito with 8 legs stands on the water surface and each leg makes a depression of radius 'a'. If the surface tension and angle of contact are 'T' and zero respectively, then the weight of mosquito is:
(A) $8Ta$
(B) $16\pi Ta$
(C) $\dfrac{{Ta}}{8}$
(D) $\dfrac{{Ta}}{{16\pi }}$

Answer 1

Hint: This is a question of surface tension. A mosquito is able to stand on the surface of water due to the surface tension applied by water on the legs of the mosquito. Here angle of contact and radius is given. We can use this to calculate weight.

Complete step by step answer
It is given that mosquitoes stand on the water surface. This is possible due to surface tension. This force acting must be equal to the weight of the mosquito for it to keep floating.
When a mosquito stands on water, there is no attraction between molecules of water and that of mosquito legs. When the force is applied by the legs on the surface, it pushes it down. Due to surface tension the water tries to regain its position which is changed due to leg force. This pushes water upward and the mosquito can stand on the water surface. We can also say that the water surface behaves as an elastic film.
Let the weight of the mosquito be ‘w’. The angle of contact is given to be zero and tension as T
So $w = 8 \times 2\pi a \times T$as there are 8 legs and a is the radius of depression
$ \Rightarrow w = 16\pi Ta$

Hence the correct option is B.

Additional information:
Surface tension can be defined as the ratio of force and length of the molecules at the surface of liquids. It is dependent on temperature. As the temperature increases the attraction force between the molecules decreases hence the liquid surface moves apart and the surface tension decreases.

Note:
Surface tension occurs on the liquid surface by which the liquid acquires minimum possible surface area. This phenomenon takes place due to intermolecular forces like Van Der Waal force between the liquid and the molecules of the container. It draws the liquid particles together. Various examples where we can see surface tension play a role is the spherical shape of liquid drops