There is a correct answer to this question, and then there is the one they want you to choose. Which one should I give you first ?
Let's start with the correct answer:
The force of gravity on any object is
(mass of the object) times (acceleration of gravity on the planet where the object is) .
The acceleration of gravity on Earth is about 9.8 m/s², so the force of gravity on this object is
(4000 kg/m³) x (0.9 m³) x (9.8 m/s²)
= (3,600 kg) x (9.8 m/s²)
= 35,280 kg-m/s² = 35,280 Newtons.
That's the force of gravity attracting this block and the Earth toward each other. It makes no difference whether the block is in your bedroom closet, in the back yard under a pile of mulch, inside a steel safe resting on a bed of styrofoam peanuts and slivered almonds, or underwater in the neighbor's pool. That's the force of gravity on this block, and it's the correct answer to the question.
It's not one of the choices, though. That's because the question is poorly written. The person who wrote the question is unclear on the concepts, and the more you work with the question, the more unclear and confused YOU'LL become.
When the block is in water, the force of gravity on it doesn't change. BUT ... there's ANOTHER force on it ... the buoyant force ... acting upward on it, and canceling part of the force of gravity.
The buoyant force is the weight of the displaced water. The displaced water is the water that has to get out of the way when you drop the block in, so the volume of displaced water is the volume of the block.
-- The volume of the block is (0.9 m³).
-- The density of water is 1000 kg/m³, so the mass of 0.9 m³ of water is 900 kg.
-- The weight of 900 kg of water is (mass) x (gravity)
= (900 kg) x (9.8 m/s²)
= 8,820 Newtons.
When the block is in water, it feels like it's that much LIGHTER, because that's the force of the water pushing UP on the block. It's the same reason why your big brother seems so light in the pool that you can pick him up and carry him.
So how heavy does this block FEEL in water ?
The force of gravity pulling down on it: 35,280 newtons The force of water pushing up on it: 8,820 newtons How heavy the block feels (the difference) 26,460 newtons
The question is written so poorly that even THIS number is not one of the choices.
Again, the thing to realize is that being in the water does NOT change the force of gravity on anything. It only creates another force, that acts against gravity.
Just like . . . When you walk up some stairs, how does it happen that you suddenly move upward, opposite to gravity. Does the force of gravity acting on you change ? No ! But you use your leg muscles to create another force in the opposite direction, that works against gravity, and makes you seem so light that you can actually move up, opposite to gravity.
Fortunately, 'force' is a vector. So if you know the strength and direction of each force, you can easily addum up and find the 'resultant' (net) force.
When we talk in vectors, one newton forward is the negative of one newton backward. Hold that thought, while I slog through the complete solution of the problem.
(100 N forward) plus (50 N backward)
= (100 N forward) minus (50 N forward)
= 50 N forward .
That's it. Is there any part of the solution that's not clear ?
Here, 2 N and 3 N forces are acting opposite to each other. In this case, the net force experience by the box would be (3-2)N = 1 N towards right. Since acceleration is directly proportional to the net force, therefore the box will experience an acceleration.
