When the wood block is dropped in the water and settles so that it floats and is no longer bobbing up and down, how do the buoyant force and gravity compare?

Buoyant force equals in magnitude the force of gravity on the wood block

Explanation:

When the object stops bobbing and floats, its weight (force exerted by gravity) equals the magnitude of the buoyant force (which in magnitude equals the weight of the fluid -in this case water- displaced by the object), but are in opposite directions so they cancel out and renders a zero net force.

When the wood block floats, its buoyant force equals in magnitude its weight (force exerted by gravity)

a. is the answer because they are not shared

can be answered using momentum.

momentum = p

p1= mass1 * velocity1

p1 = p2

therefore

p1 = 6kg * 4m/s

p1 = 24kgm/s

p2=m2 * v2

24 kgm/s = 7kg * v2

v2 = 24 kgm/s / 7kg

v2= 3.42 m/s