A soap bubble of surface tension 0.04 ~N / m is blown to a diameter of 7 cm. If (15000-x) μ J of work is done in blowing it further to make its diameter 14 cm, then the value of x is \_\_\_\_ . ( π=22 / 7 )

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Soap bubble has two surfaces. Work done:

W = \Delta A \times \sigma

Initial radius:

r_i = 3.5

cm = 0.035 m, Final radius:

r_f = 7

cm = 0.07 m
Change in surface area (both surfaces):

\Delta A = 8\pi(r_f^2 - r_i^2) = 8\pi(0.07^2 - 0.035^2)

\Delta A = 8\pi(0.0049 - 0.001225) = 8\pi \times 0.003675 = 0.0294\pi

m²

W = 0.0294\pi \times 0.04 = 0.001176\pi

J =

0.001176 \times \frac{22}{7} = 0.003696

J = 3696 μJ
Therefore:

x = 15000 - 3696 = 11304

A soap bubble of surface tension 0.04 ~N / m is blown to a diameter...

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