Question

. A soap film is trapped between a frame and a wire of length 10 cm as show if the surface tension is given as 0.0049 N/m, what will be the value of m (in mg)such that the wire remains in equilibrium? a) 0.1 b) c) 10 d) 100
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Answer 1

Condition for the wire to be in equilibrium:

Force exerted by the film on the wire due to surface tension (acting upwards) must be equal to the downward force due to the weight of the wire (acting downwards).

Given,

• Surface tension(σ) = 0.0049 N/m

• Length (l) = 10 cm = 0.1 m

• Acceleration due to gravity (g) = 9.8 m/s

We know the equation:

$\huge{\boxed{\bold{\sf{m=\dfrac{2 \sigma l}{g}}}}}$

Applying values to the equation:

$\sf{\implies m=\dfrac{2 \times 0.0049\times 0.1}{9.8}}$

$\sf{\implies m=\dfrac{0.0098}{9.8}}$

$\sf{\implies m=0.0001 \ g }$

$\sf{\implies m=0.1 \ mg }$

$\huge{\boxed{\bold{\sf{\therefore m=0.1 \ mg }}}}$

Answer is Option (a) 0.1