A solid sphere of radius \(r\) is floating at the interface of two immiscible liquids of densities \(\rho_1\) and \(\rho_2\) where \(\rho_2 >\rho_1 \), half of its volume lying in each zone. The height of the upper liquid column from the interface of the two liquids is \(h\).

Find the force exerted on the sphere by contact with the upper liquid layer.

**Details**

- atmospheric pressure = \(p_0\)
- acceleration due to gravity is \(g\)

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