A 4.0-kg cylinder of solid iron is supported by a string while submerged in water. What is the tension in the string? The density of iron is 7860 kg/m3 and that of water is 1000 kg/m3.

A) 34 N B) 2.5 N C) 24 N D) 40 N E) 20 N

It is A, 34N

Well, well, this seems like a bit of an aquatic adventure! Let's dive right into it, shall we?

To find the tension in the string, we need to consider the forces acting on the cylinder. First, we have the weight of the cylinder, given by the formula:

Weight = mass x gravity

The mass of the cylinder is 4.0 kg and the acceleration due to gravity is approximately 9.8 m/s^2, which results in a weight of 39.2 N. This weight will be countered by two forces: the buoyant force and the tension in the string.

The buoyant force can be calculated using Archimedes' principle, which states that the buoyant force is equal to the weight of the fluid displaced by the object. In this case, the fluid is water, so we need to find the volume of the cylinder and multiply it by the density of water:

Volume = mass / density

The mass of the cylinder is still 4.0 kg, but the density of iron is given as 7860 kg/m^3. Therefore, the volume is 0.000509 m^3. Multiplying this by the density of water, which is 1000 kg/m^3, we get a buoyant force of 0.509 N.

So, now we have two forces: the weight of the cylinder (39.2 N) and the buoyant force (0.509 N) acting in opposite directions. The tension in the string is the force balancing these two forces, which means it will be equal to their difference:

Tension = Weight - Buoyant force
Tension = 39.2 N - 0.509 N
Tension ≈ 38.7 N

Well, it seems I took a bit too long to reach the answer. As a clown bot, I do have a tendency to get carried away with explanations. So, let's cut straight to the chase: the tension in the string is approximately 38.7 N.

Wait a minute, that's not even an option! Oh, you tricky test-makers! Well, I guess we have to settle for the closest option available. In this case, the closest option to 38.7 N is option D) 40 N.

So, my aquatic adventurer, the tension in the string is approximately 40 N. Safe travels!

To calculate the tension in the string, we need to consider the forces acting on the cylinder. The two forces we need to consider are the weight of the cylinder and the buoyant force acting on the cylinder.

The weight of the cylinder can be calculated using the formula: Weight = mass x gravity. In this case, the mass of the cylinder is 4.0 kg and the acceleration due to gravity is approximately 9.8 m/s^2.

Weight = 4.0 kg x 9.8 m/s^2 = 39.2 N

The buoyant force can be calculated using the formula: Buoyant force = density of fluid x volume of fluid displaced x gravity. In this case, the fluid is water, and we need to calculate the volume of water displaced by the cylinder.

The volume of water displaced is equal to the volume of the cylinder, which can be calculated using the formula: Volume = mass / density. In this case, the mass of the cylinder is 4.0 kg and the density of iron is 7860 kg/m^3.

Volume = 4.0 kg / 7860 kg/m^3 = 0.000508 m^3

Now we can calculate the buoyant force:

Buoyant force = density of water x volume of water displaced x gravity

Buoyant force = 1000 kg/m^3 x 0.000508 m^3 x 9.8 m/s^2 = 5 N

Now we can calculate the tension in the string. Since the cylinder is in equilibrium, the tension in the string is equal to the weight of the cylinder minus the buoyant force:

Tension = Weight - Buoyant force = 39.2 N - 5 N = 34.2 N

Therefore, the correct answer is A) 34 N.

To find the tension in the string, we need to consider the forces acting on the iron cylinder.

1. Weight of the cylinder: The weight of the cylinder can be calculated using the formula W = mg, where W is the weight, m is the mass, and g is the acceleration due to gravity. In this case, the mass of the cylinder is given as 4.0 kg, and the acceleration due to gravity is approximately 9.8 m/s^2. Therefore, the weight of the cylinder is W = (4.0 kg) * (9.8 m/s^2).

2. Buoyant force: The iron cylinder is submerged in water, so it experiences an upward buoyant force equal to the weight of the water it displaces. The volume of water displaced can be calculated using the formula V = m/ρ, where V is the volume, m is the mass, and ρ is the density of the fluid. In this case, the density of water is given as 1000 kg/m^3, and the mass of the cylinder is 4.0 kg. Therefore, the volume of water displaced is V = (4.0 kg) / (1000 kg/m^3).

3. Tension in the string: The tension in the string is equal to the difference between the weight of the cylinder and the buoyant force. It is given by T = W - B, where T is the tension, W is the weight of the cylinder, and B is the buoyant force.

Now, let's calculate the tension in the string:

W = (4.0 kg) * (9.8 m/s^2) = 39.2 N

V = (4.0 kg) / (1000 kg/m^3) = 0.004 m^3

B = (density of water) * (volume of water) * (acceleration due to gravity) = (1000 kg/m^3) * (0.004 m^3) * (9.8 m/s^2)

T = 39.2 N - [(1000 kg/m^3) * (0.004 m^3) * (9.8 m/s^2)]

After calculating the expression, we get:

T = 39.2 N - 39.2 N = 0 N

Therefore, the tension in the string is 0 N. None of the given answer choices (A, B, C, D, E) are correct.

the tension is just the weight of the iron, minus the weight of the water displaced.