Question

an object sinks to the bottom of a container filled with water.what is the relationship between the weight of the object and the buoyant force acting on it?

Answer 1

If the object sinks, then it must be heavier than the weight of the water
it displaces ... heavier than the buoyant force acting on it. 

If the buoyant force were equal or greater than the object's weight, then
the object would rise to the surface in water.

Answer 2

Answer: The buoyant force will be directly proportional to the weight of the object.

$F_B=\rho\times \frac{weight}{\rho_o}$

Explanation:

The buoyant force acting on the object immersed in liquid is given by:

$F_B=\rho gV$

$\rho$ = density if the liquid

V = Volume of the liquid displaced by the object

If an object sinks to the bottom of a container filled with water.This mans that volume displaced by the object is equal tho the volume of the object ,$V=V_o$ .

$F_B=\rho gV$,

$F_B=\rho gV_o$

Density of the object:

=$\rho_o=\frac{\text{mass of the object}}{\text{Volume of the object}(V_o)}$

$F_B=\rho gV_o=\rho g\frac{Mass}{\rho_o}$

Weight of the object =$Mass\times g$

Since, weight is directly proportional to the mass of the object and mass of the object. So the buoyant force will be directly proportional to the weight of the object.

$F_B=\rho\times \frac{weight}{\rho_o}$