TS EAMCET · Physics · Mechanical Properties of Fluids
If \(W_1\) is the work done in increasing the radius of a soap bubble from ' \(r\) ' to ' \(2 r\) ' and \(W_2\) is the work done in increasing the radius of the soap bubble from ' \(2 r\) ' to ' \(3 r\) ', then \(W_1: W_2=\)
- A \(3: 5\)
- B \(1: 1\)
- C \(2: 3\)
- D \(3: 4\)
Answer & Solution
Correct Answer
(A) \(3: 5\)
Step-by-step Solution
Detailed explanation
\(W = T \cdot 2 \cdot \Delta A = T \cdot 2 \cdot 4\pi (R_f^2 - R_i^2)\) \(W_1 = T \cdot 8\pi ((2r)^2 - r^2) = T \cdot 8\pi (4r^2 - r^2) = T \cdot 8\pi (3r^2) = 24\pi T r^2\) \(W_2 = T \cdot 8\pi ((3r)^2 - (2r)^2) = T \cdot 8\pi (9r^2 - 4r^2) = T \cdot 8\pi (5r^2) = 40\pi T r^2\)…
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