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Although the fact may be obscured by the presence of a liquid, the basic condition for equilibrium still holds: The net force on the ball must be zero.

Here are the steps that I went through:

Compute the mass m_f of the fluid displaced by the object when it is entirely submerged.

Express your answer in terms of p_f, v, m_b, and g.

m_f = p_f*V

f_buoyant = p_f* V * g

How do I get from here to finding the tension?

Thanks.