This question is two problems in one ... at least. Ordinarily, I wouldn't
bother with it, but the lure of that glorious, bountiful 5 points at the finish
line is too strong to resist.
I need to point out that there is an inconsistency in the question, and it's
technically worded wrong. The question says
"What is the force of gravity (the weight) in water ?"
When the block is in water, the force of gravity on it and its apparent
weight are two different things. The force of gravity on you when you're
floating on your back in the lake is exactly the same as the force of gravity
on you when you're standing on the beach. The force of gravity on the
steel block doesn't depend on what's around it, and it doesn't change.
If the force of gravity on the block is one million tons, then it's a million
tons whether the block is in air, in water, in molasses or in chicken soup.
The difference is that in water, there's ANOTHER force on it ... the
buoyant force of the surrounding fluid ... that cancels part of the force
of gravity, making the block seem to weigh less in water. The question
isn't asking for the force of gravity on the block. It's asking for what the
block SEEMS to weigh when it's in water.
Now that we've gotten that out of the way, here's how we need to
untangle the question in order to answer it:
-- The weight of the block in water is
(its weight OUT of water) minus (the buoyant force on it IN the water).
We'll need to find both of those.
-- In order to find its weight out of water, we need to find its mass.
-- In order to find its mass, we need to massage the given volume and density.
Let's begin:
Density = (mass) / (volume)
Multiply each side by (volume): Mass = (density) x (volume) =
(7,840 kg/m³) x (0.08 m³)
Mass = 627.2 kg.
Weight (out of water) = (mass) x (acceleration of gravity)
Acceleration of gravity on Earth = 9.8 m/s² .
Weight of the steel block out of water = (627.2 kg) x (9.8 m/s²)
Weight = 6,146.6 newtons .
(about 1,382 pounds)
Now all we need is the buoyant force on the block when it's in the water.
The buoyant force on it is the weight of an equal volume of water.
Volume of the block = 0.08 m³ = 80 liters.
Density of water = 1 kg/liter
Weight of water = (1 kg/liter) x (9.8 m/s²) = 9.8 newtons/liter
Mass of 0.08 m³ of water = 80 kg
Weight of 0.08 m³ of water = (80 kg) x (9.8 m/s²) = 784 newtons
Weight of the block in water = (6,146.6 - 784) = 5,362.6 newtons
(about 1,206 pounds)