A soap bubble is blown to a diameter of 7 cm. 36960 erg of work is done in blowing it further. If surface tension of soap solution is 40 dyne/cm then the new radius is _______ cm.

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Solution

Q.
A soap bubble is blown to a diameter of 7 cm. 36960 erg of work is done in blowing it further. If surface tension of soap solution is 40 dyne/cm then the new radius is _______ cm. Take $(π = \frac{22}{7})$ [2024]

Ans.
(7) $Δ W = 2 T \cdot 4 π r_{2}^{2} - 2 T \cdot 4 π r_{1}^{2}$

$r_{2}^{2} - r_{1}^{2} = \frac{Δ W}{8 T π} = \frac{36960 \times 7}{8 \times 40 \times 22} = 36.75$

$r_{2}^{2} = 36.75 + \frac{49}{4} = 49 \Rightarrow r_{2} = 7 cm$

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