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Question

A rectangular film of liquid is extended from (2 cm×8 cm) to (4 cm×16 cm). If work done is 5 ×104 J, value of the surface tension of the liquid is

A
0.06 N/m
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B
0.08 N/m
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C
0.05 N/m
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D
0.09 N/m
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Solution

The correct option is C 0.05 N/m
Given , work done (W)=5×104 J
Change in area (ΔA)=(4 cm×16 cm)(2 cm×8 cm)
=48 cm2=48×104 m2
We know from the definition of surface energy that
Surface energy (S)=Work done (W)change in area (ΔA)
Since the film has two surfaces, the change in area
ΔA=2×48×104 m2
S=5×1042×48×104
S=0.05 N/m2
The value of surface energy (S) of a liquid is numerically equal to the value of surface tension.
we can say that, surface tension of the liquid is 0.05 N/m
Hence, option (c) is the correct answer.

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