A 48-N object floats in a pool. If 75% of the volume of the object is immersed in the water, which statement is true about the buoyant force FB on the object?

A. FB=48N
B. FB=36N
C. FB=64N
D. FB=12N
E. This is not possible to answer with the information given.

Do/Dw = 0.75.

Do/1 = 0.75, Do = 0.75g/cm^3 = Density of the object.

M*g = 48 N. M = 48/g = 48/9.8 = 4.90 kg. = 4900g = Wt. of object.

Vo = 4900g/(0.75g/cm^3) = 6533.3 cm^3 = Vol. of object.

0.75 * 6533.3 = 4900 cm^3 immersed = Vol. of water displaced.

4900cm^3 * 1g/cm^3 = 4900g = 4.9kg of water displaced.

Fb = M*g = 4.9 * 9.8 = 48 N.

E. This is not possible to answer with the information given.

Because the buoyant force depends on the density of the fluid and the volume of the object submerged, we need to know the density of the fluid in order to calculate the buoyant force.

To find the buoyant force FB on an object, we can use the formula:

FB = ρVg

Where:
FB is the buoyant force,
ρ is the density of the fluid (water in this case),
V is the volume of the fluid displaced by the object, and
g is the acceleration due to gravity.

Given that 75% of the volume of the object is immersed in the water, we can determine the volume of the fluid displaced by the object. Let's call this volume Vd.

Vd = 75% of the volume of the object

Now, we know that the buoyant force FB is equal to the weight of the fluid displaced by the object. In this case, it is equal to the weight of the water displaced by the object.

The weight of water displaced = volume of water displaced × density of water × acceleration due to gravity

Given that the weight of the object is 48N, we can determine the volume of the object using the formula:

Volume of the object = Weight of the object / Density of the fluid

Since the density of water is 1000 kg/m³ (approximately), and the weight of the object is 48N, we get:

Volume of the object = 48N / 1000 kg/m³

Now, we can substitute this value to calculate the volume of the fluid displaced by the object:

Vd = 75% × Volume of the object

Finally, we can calculate the buoyant force FB using the formula:

FB = Volume of the fluid displaced × Density of the fluid × acceleration due to gravity

Now, let's perform the calculations:

Density of water = 1000 kg/m³
Acceleration due to gravity = 9.8 m/s²

Volume of the object = 48N / 1000 kg/m³
Vd = 75% × Volume of the object

FB = Vd × Density of water × acceleration due to gravity

After performing these calculations, we will be able to determine which statement is true about the buoyant force FB on the object.

To determine the correctness of each statement about the buoyant force on the object, we need to understand the relationship between buoyant force and the volume of the object immersed in the water.

The buoyant force (FB) is the upward force exerted on an object immersed in a fluid, such as water, and it is equal to the weight of the fluid displaced by the object. According to Archimedes' principle, the buoyant force is proportional to the volume of the fluid displaced.

In this case, the object is floating in the water, which means the buoyant force is equal to the weight of the object. The weight of the object is given as 48 N.

The statement in option A, FB = 48 N, implies that the buoyant force is equal to the weight of the object. Since the object is floating, this statement is true.

The statement in option B, FB = 36 N, suggests the buoyant force is less than the weight of the object. However, for a floating object, the buoyant force is equal to the weight of the object. Thus, option B is incorrect.

The statement in option C, FB = 64 N, implies that the buoyant force is greater than the weight of the object. Again, for a floating object, the buoyant force is equal to the weight of the object. Therefore, option C is incorrect.

The statement in option D, FB = 12 N, suggests that the buoyant force is lower than the weight of the object. However, since the object is floating, the buoyant force must be equal to the weight of the object. Thus, option D is incorrect.

Based on the explanations above, the correct answer is option A: FB = 48 N.