Answer:
When an object floats in water, the weight of the object is equal to the buoyant force acting on it. The buoyant force is equal to the weight of the displaced water, which is equal to the volume of the displaced water times the density of water times the acceleration due to gravity. Therefore, we have:
Weight of object = Buoyant force
m_object * g = V_submerged * density_water * g
where m_object is the mass of the object, V_submerged is the volume of the object that is submerged in water, and density_water is the density of water.
We can rearrange this equation to solve for the density of the object:
density_object = m_object / V_object
where V_object is the total volume of the object.
We can substitute the expression for m_object from the first equation into the second equation and simplify to get:
density_object = density_water * V_submerged / (V_object - V_submerged)
We are given that 35% of the volume of the object is submerged in water, so we know that:
V_submerged = 0.35 * V_object
Substituting this expression into the equation for density_object, we get:
density_object = density_water * 0.35 * V_object / (V_object - 0.35 * V_object)
Simplifying this expression, we get:
density_object = density_water * 0.35 / 0.65
Substituting the density of water, which is 1000 kg/m^3, we get:
density_object = 1000 kg/m^3 * 0.35 / 0.65 = 540.54 kg/m^3
Therefore, the density of the object is 540.54 kg/m^3.