A frame made of metallic wire enclosing a surface area A is covered with a soap film. If the area of the frame of metallic wire is reduced by $50 %$ , the energy of the soap film will be changed by

100 %

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75 %

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50 %

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25 %

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Solution

The correct option is B $50 %$
Area of one side of frame $= A$
But metallic wire frame having soap film has two surfaces.
Thus total surface area of the frame $= 2 A$
Energy of soap film, $E = 2 A T$ (where $T$ is the surface tension of soap film)
Now the surface area of one side is reduced to half i.e $A^{'} = \frac{A}{2}$
$∴$ $E^{'} = 2 A^{'} T = 2 T \times \frac{A}{2} = A T$
Percentage change in energy $= \frac{E - E^{'}}{E} \times 100 = \frac{2 A T - A T}{2 A T} \times 100 = 50$ %

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