JEE Main 20146 April
- Exam
- JEE Main
- Year
- 2014
- Date
- 6 April
- Subject
- Physics
- Chapter
- Mechanical Properties of Fluids
JEE Main 2014 · 6 April · Physics · Mechanical Properties of Fluids
On heating water, bubbles being formed at the bottom of the vessel...
On heating water, bubbles being formed at the bottom of the vessel detatch and rise. Take the bubbles to be spheres of radius R and making a circular contact of radius r with the bottom of the vessel. If r << R, and the surface tension of water is T, value of r just before bubbles detatch is :
(density of water is )
(density of water is )
Options
- A
- B{\text{R}}^{2} \sqrt{\dfrac{{ρ}_{\text{w}} \text{g}}{6 T}}
- C{\text{R}}^{2} \sqrt{\dfrac{{ρ}_{\text{w}} \text{g}}{T}}
- D{\text{R}}^{2} \sqrt{\dfrac{{3 ρ}_{\text{w}} \text{g}}{T}}
Correct answer
A.
Step-by-step solution
When the bubble gets detached,
Buoyant force = force due to surface tension
∫ \text{T} \times dl \text\sin \theta = \dfrac{4}{3} \pi {\text{R}}^{3} {ρ}_{\text{w}} \text{g}
Buoyant force = force due to surface tension
∫ \text{T} \times dl \text\sin \theta = \dfrac{4}{3} \pi {\text{R}}^{3} {ρ}_{\text{w}} \text{g}