A light cylindrical vessel is kept on a horizontal surface. Its base area is A. A hole of cross-sectional area a is made just at its bottom side. The minimum coefficient of friction necessary for sliding of the vessel due to the impact force of the emerging liquid is x × 10⁻³. Find x (a ≪ A). Given a/A = 2 × 10⁻³.
Physics · Mixed Chapter
JEE Mains

Question

A light cylindrical vessel is kept on a horizontal surface. Its base area is A. A hole of cross-sectional area a is made just at its bottom side. The minimum coefficient of friction necessary for sliding of the vessel due to the impact force of the emerging liquid is x × 10⁻³. Find x (a ≪ A). Given a/A = 2 × 10⁻³.

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: Liquid leaves the hole horizontally at efflux speed v=√(2gh), producing horizontal reaction force F=ṁv=ρa v²=2ρagh. Step 2: Vessel mass is negligible; the weight of the contained water is approximately ρA h g. Maximum static friction is μρA h g. Step 3: Threshold is μρA h g=2ρa h g, giving μ_min=2a/A. Step 4: With a/A=2×10⁻³, μ_min=4×10⁻³, hence x=4.