Question

A soap film is created in a small wire frame as shown in the figure. The sliding wire of mass m is given a velocity u to the right and assume that u is small enough so that film does not break. Plane of the film is horizontal and surface tension is T. Then time to regain the original position of wire is equal to :

• A. $\frac{um}{Tl}$
• B. $\frac{Tl}{um}$
• C. $\frac{m{u}^2}{Tl}$
• D. It will never regain original position

Answer 1

The correct option is A $\frac{um}{Tl}$

Since there are two films formed due to surface tension on the wire frame,
$F=2\left(Tl\right)$
$\therefore ma=2Tl$
$\therefore a=\frac{2Tl}{m}$
Using the one dimensional kinematics eqn
$v=u+at$
we get, $0=u-at=u-\frac{2Tl}{m}t$ since velocity decreases and becomes zero and then the frame moves in the opposite direction.
$\therefore t=\frac{um}{2Tl}$
Total time to regain the original position $T=2t=\frac{2um}{2Tl}=\frac{um}{Tl}$