Two hemispheres of radius R combined together by two minimum forces ' F ' to form a sphere (completely filled with water) as shown in figure. A small pin hole of radius a at top of the spher

Question

Two hemispheres of radius R combined together by two minimum forces ' F ' to form a sphere (completely filled with water) as shown in figure. A small pin hole of radius a at top of the sphere as shown in figure. If the system is in equilibrium at $tan θ = \frac{x}{2}$ . Find the value of x . (gravity is present and no other support is given to hemispheres) Neglect atmospheric pressure.

Question figure

TestHub · Accepted Answer

2 F cos θ = m g F cos θ = 2 m g ​ F sin θ = ( ρ g R ) π R 2 tan θ = m g 2 ρ g π R 3 ​ m = ρ 3 4 ​ π R 3 tan θ = 4/3 2 ​ = 2 3 ​

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