Question

The amount of work done in blowing a soap bubble such that its diameter increases from d to D is (T= surface tension of the solution)

• A. $4 \pi \left( D ^ { 2 } - d ^ { 2 } \right) T$
• B. $8 \pi \left( D ^ { 2 } - d ^ { 2 } \right) T$
• C. $\pi \left( D ^ { 2 } - d ^ { 2 } \right) T$
• D. $2 \pi \left( D ^ { 2 } - d ^ { 2 } \right) T$

Answer 1

Answer: (D)

$2 \pi \left( D ^ { 2 } - d ^ { 2 } \right) T$

Answer 2

$W = T \times 8 \pi \left( r _ { 2 } ^ { 2 } - r _ { 1 } ^ { 2 } \right) = T \times 8 \pi \left( \frac { D ^ { 2 } } { 4 } - \frac { d ^ { 2 } } { 4 } \right)$

$= 2 \pi \left( D ^ { 2 } - d ^ { 2 } \right) T$