Air (density $\rho$ ) is being blown on a soap film (surface tension $T$ ) by a pipe of radius $R$ with its opening right next to the film. The film is deformed and a bubble detaches from the film when the shape of the deformed surface is a hemisphere. Given that the dynamic pressure on the film due to the air blown at speed $v$ is $\frac{1}{2} \rho v^{2}$, the speed at which the bubble formed is
Air (density $\rho$ ) is being blown on a soap film (surface tension $T$ ) by a pipe of radius $R$ with its opening right next to the film. The film is deformed and a bubble detaches from the film when the shape of the deformed surface is a hemisphere. Given that the dynamic pressure on the film due to the air blown at speed $v$ is $\frac{1}{2} \rho v^{2}$, the speed at which the bubble formed is
- [KVPY 2018]
- A
$\frac{T}{\sqrt{\rho R}}$
- B
$\sqrt{\frac{2 T}{\rho R}}$
- C
$\sqrt{\frac{4 T}{\rho R}}$
- D
$\sqrt{\frac{8 T}{\rho R}}$
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- [JEE MAIN 2018]
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