Question

Consider a U-shaped frame with a sliding wire of length $\ell$ and mass 'm' on its arm. It is dipped in a soap solution, taken out and placed in vertical position such that a thin film is formed on it as shown in figure. Find maximum value of m so that wire does not descend: (Surface tension of soap solution is S)

• A. $\frac{2S\ell }{g}$
• B. $\frac{S\ell }{g}$
• C. $\frac{S\ell }{2g}$
• D. $\frac{S\ell }{4g}$

Answer 1

The correct option is A

$\frac{2S\ell }{g}$

Sliding wire length = $\ell$
For wire to maintain its position, it should be in equilibrium
$\Rightarrow 2F=mg$
(soap film form two surfaces)
'F' is the surface tension force exerted by each surface of soap film.

$\therefore 2S\ell =mg$

$\Rightarrow \therefore m=\frac{2S\ell }{g}$

Why this question? Tip: A soap film on a U-shaped frame will form a double surface, each surface will pull the wire with force $F=S\ell$