Can't get correct answer

An object weighing 340 N in air is immersed in water after being tied to a string connected to a balance. The scale now reads 260 N. Immersed in oil, the object weighs 290 N.

(a) Find the density of the object.
kg/m3
(b) Find the density of the oil.
kg/m3

The volume of water displaced weighs 80 N, and has a mass of 80 N/g = 8.16 kg. That amount of water occupies 8.16 liters, or 8.16*10^-3 m^3, and equals the volume of the object. So the object's density is

[340 N/g]/8.16*10^-3 m^3
= 4250 kg/m^3

The weight reduction in oil is 5/8 of the weight reduction in water, so the oil has 50/80 of the density of water, or 625kg/m^3

To find the density of the object and the oil, we can use the principle of buoyancy.

The buoyant force experienced by an object submerged in a fluid is equal to the weight of the fluid displaced by the object.

Let's work through each part of the question step-by-step:

(a) First, we need to calculate the buoyant force experienced by the object when it is immersed in water. The difference in weight before and after the immersion gives us this value.

The initial weight of the object in air is 340 N, and when immersed in water, the scale reads 260 N. So, the buoyant force in water is:

Buoyant force in water = Weight in air - Weight in water
= 340 N - 260 N
= 80 N

The buoyant force is also equal to the weight of the water displaced by the object. Hence, the mass of the water displaced can be calculated using the formula:

Buoyant force = density of water * volume of water displaced * g
80 N = density of water * volume of the object * g

Since the volume of the water displaced is the same as the volume of the object, we can rewrite the equation as:

80 N = density of water * volume of the object * g

Now, rearranging the equation to solve for the density of the object:

density of object = 80 N / (volume of the object * g)

To find the volume of the object, we need to utilize the fact that density is defined as mass divided by volume. Rearranging this equation:

volume of the object = mass of the object / density of the object

We don't know the mass of the object, but we can use its weight to calculate it:

mass of the object = weight of the object / g

Substituting this back into the equation for volume:

volume of the object = (weight of the object / g) / density of the object

You might need to know the value of acceleration due to gravity (g), which is approximately 9.8 m/s^2.

Once you have the volume of the object, you can substitute it back into the equation to find the density of the object:

density of object = 80 N / ((weight of the object / g) / density of the object)

(b) To find the density of the oil, we follow the same procedure as in part (a), but this time using the weight of the object when immersed in oil. The buoyant force in oil is:

Buoyant force in oil = Weight in air - Weight in oil
= 340 N - 290 N
= 50 N

Again, the buoyant force is equal to the weight of the oil displaced by the object. So, we can set up the similar equation as before:

50 N = density of oil * volume of the object * g

Solving for the density of the oil:

density of oil = 50 N / (volume of the object * g)

Using the procedure outlined above, substitute the volume of the object to find the density of the oil.

Remember to convert the weight in Newtons to mass in kilograms, using the formula: mass = weight / g.

Once you have the volume of the object, substitute it back into the equation to find the density of the oil:

density of oil = 50 N / ((weight of the object / g) / density of the oil)

I hope this helps! Let me know if you have any further questions.