a 2.0 kg solid mass has an apparent weight 12.34N when totally immersed in water. Calculate the apparent weight of the body when totally immersed in a liquid of density 0.78

2 kg * 9.81 = 19.62 N weight

loses (19.62-12.34) = 7.28 N in water

7.28 N /9.81 = .7421 Kg of water displace

.7421 kg * 1 m^3/1000 kg = 7.421 * 10^-4 m^3 = volume of mass

mass of light fluid displaced =
7.421 *10^-4 m^3 * .78 * 10^3
= .579 kg
weight of light fluid displaced =
.579*9.81 = 5.68 N of light fluid displaced
so apparent weight = 19.62 - 5.68 = 13.9 Newtons
---------------------------
OR MORE EASILY IF I had thought a little
2 kg * 9.81 = 19.62 N weight

loses (19.62-12.34) = 7.28 N in water
but in our fluid it will lose .78 * 7.28 = 5.68 N
19.62 - 5.68 = 13.9 N

thanks Damon

Well, well, well, it looks like we have ourselves a buoyancy question! Let's dive right in, shall we?

The apparent weight of an object submerged in a fluid depends on the buoyant force acting on it, which is equal to the weight of the fluid displaced by the object. So, to find the apparent weight, we need to determine the buoyant force for both scenarios.

First, let's deal with the body submerged in water. The buoyant force can be calculated using Archimedes' principle, which states that the buoyant force equals the weight of the fluid displaced.

Since the body is completely submerged, it displaces a volume of water equal to its own volume. The density of water is approximately 1000 kg/m³, so the volume of the body is 2.0 kg / 1000 kg/m³ = 0.002 m³.

Using the buoyant force formula: Buoyant force = Density of fluid × Volume × Gravitational acceleration, we can calculate the buoyant force in water.

Buoyant force (in water) = 1000 kg/m³ × 0.002 m³ × 9.8 m/s² = 19.6 N

Now, let's move on to the second scenario where the body is immersed in a liquid with a density of 0.78. We'll follow the same steps as before.

The volume of the body remains constant, so the volume of liquid displaced is still 0.002 m³.

Buoyant force (in liquid) = 0.78 kg/m³ × 0.002 m³ × 9.8 m/s² = 0.01524 N

So, the apparent weight of the body when fully immersed in the liquid is 0.01524 N.

I hope that brought a little buoyant smile to your face!

To solve this problem, we will need to use Archimedes' principle, which states that the buoyant force acting on a submerged object is equal to the weight of the displaced fluid.

Given:
Mass of the solid, m = 2.0 kg
Apparent weight in water, F_app_water = 12.34 N
Density of the liquid, ρ = 0.78 kg/L

Step 1: Find the volume of the solid.
The formula to calculate the volume of a solid is given by:
Volume (V) = Mass (m) / Density (ρ)

Converting density from kg/L to kg/m^3:
ρ = 0.78 kg/L = 0.78 x 1000 kg/m^3 = 780 kg/m^3

Now, substitute the known values:
V = 2.0 kg / 780 kg/m^3
V ≈ 0.0026 m^3

Step 2: Find the weight of the displaced liquid.
The weight of the displaced liquid is equal to the weight of the solid when it is fully immersed in the liquid.
Weight of the displaced liquid, F_displaced_liquid = m x g

Assuming the acceleration due to gravity, g = 9.8 m/s^2, we can calculate the weight of the displaced liquid:
F_displaced_liquid = 2.0 kg x 9.8 m/s^2
F_displaced_liquid = 19.6 N

Step 3: Find the apparent weight in the new liquid.
The apparent weight is the difference between the weight of the solid in air and the weight of the displaced liquid:
Apparent weight = Weight in air - Weight of displaced liquid

Weight in air = Mass x g
Weight in air = 2.0 kg x 9.8 m/s^2
Weight in air = 19.6 N

Apparent weight = 19.6 N - 19.6 N
Apparent weight = 0 N

Therefore, the apparent weight of the body when totally immersed in a liquid of density 0.78 kg/L is 0 N.

To calculate the apparent weight of the body when totally immersed in a liquid of density 0.78, we need to understand the concept of buoyancy and how it affects the apparent weight of an object.

Buoyancy is the upward force exerted by a fluid on an immersed object. According to Archimedes' principle, this force is equal to the weight of the fluid displaced by the object.

Here's how you can calculate the apparent weight of the body:

1. Determine the volume of the solid mass:
- The volume of the solid mass can be calculated using its density and mass. In this case, the mass is 2.0 kg, so we need the density.
- Since the density of the solid mass is not provided, we need more information or assume a specific value to proceed with the calculations.

2. Determine the volume of the fluid displaced:
- The volume of the fluid displaced by the object is equal to the volume of the object itself.
- Multiply the density of the liquid (0.78 kg/L) by the volume of the object to calculate the mass of the displaced fluid.

3. Calculate the weight of the displaced fluid:
- Multiply the mass of the displaced fluid by the acceleration due to gravity (9.8 m/s^2) to calculate the weight of the fluid.

4. Calculate the apparent weight:
- Subtract the weight of the displaced fluid from the weight of the object in air to get the apparent weight of the body when immersed in the liquid.

Without the value for the density of the solid mass, it is not possible to provide an exact answer. However, by following the steps above, you will be able to calculate the apparent weight once the necessary information is available.