Question

A soap film of surface tension $3\times {{10}^{-2}}N{{m}^{-1}}$formed in a rectangular frame, can support a straw. If the length of the film is 10cm, then the mass of the straw that film can support is:
(A) 0.06g
(B) 0.6g
(C ) 6g
(D) 60g

Answer 1

Hint: Here the weight of the straw must be equal to the force due to surface tension. The weight of the straw is the product of mass and the acceleration. And the force acting is the force due to the surface tension. Then equating those two terms and then rearranging the equation we will get the mass of the straw.

Complete step by step answer:
In this problem the weight of the straw must be equal to the force due to surface tension.
Let us consider that the mass of the straw be m and the acceleration here is the acceleration due to gravity acting vertically downwards.
Then the weight of the straw is mg.
We know that surface tension is the force per unit length.
Then calculating the force due to surface tension we get,
\[F=2Tl\]
Where, T is the surface tension and l is the length of the film.
Since the soap film has two surfaces the surface tension is considered as 2T.
Thus on equating the two values we get,
$mg=2Tl$
Rearranging the equation becomes,
$m=\dfrac{2Tl}{g}$
Then substituting the values in the above equation,
$m=\dfrac{2\times 3\times {{10}^{-2}}\times 10\times {{10}^{-2}}}{10}$
$m=0.6g$

So, the correct answer is “Option b”.

Note: We can in general describe surface tension as the force per unit length. Hence the unit of surface tension is Newton per metre. In the case of a rectangular soap film it has two surfaces. So its surface tension is equal to two times the surface tension on one side.