A body of density 9.0g/cm^3 appears to have a mass of 27.0g in a liquid of density 1.2g/cm^3.what is the volume of the solid
force up = 1.2 *v * g + 27.0 * g
force down = 9.0 * v * g
no acceleration so force up = forcedown
9.0 v = 1.2 v + 27
7.8 v = 27
To find the volume of the solid, we can use the formula:
Volume = Mass / Density
Given that the mass of the body is 27.0g and the density of the body is 9.0g/cm^3, we can substitute these values into the formula:
Volume = 27.0g / 9.0g/cm^3
Now, we need to be aware that the density of the liquid is given as 1.2g/cm^3. This means that the body is floating, since the density of the liquid is less than the density of the body.
In order to solve for the volume correctly, we need to take into account the Archimedes' principle, which states that the buoyant force on an object submerged in a fluid is equal to the weight of the fluid that the object displaces. In other words, the weight of the fluid displaced is equal to the weight of the object.
So, the weight of the fluid displaced is:
Weight of fluid displaced = Mass of fluid displaced × Gravity
Since the density of the fluid is 1.2g/cm^3 and the volume of the fluid displaced is the same as the volume of the body, we can calculate the mass of the fluid displaced using the formula:
Mass of fluid displaced = Density of fluid × Volume of fluid displaced
Now, applying Archimedes' principle by setting the weight of the fluid displaced equal to the weight of the body:
Mass of fluid displaced × Gravity = Mass of body × Gravity
Substituting the formulas for mass of fluid displaced and mass of body:
Density of fluid × Volume of fluid displaced × Gravity = Density of body × Volume of body × Gravity
Since the acceleration due to gravity (g) cancels out, we are left with:
Density of fluid × Volume of fluid displaced = Density of body × Volume of body
Substituting the known values:
1.2g/cm^3 × Volume of fluid displaced = 9.0g/cm^3 × Volume of body
Since the density of the fluid is less than the density of the body, the volume of fluid displaced will be equal to the volume of the body.
Thus, we can rewrite the equation as:
1.2g/cm^3 × Volume of body = 9.0g/cm^3 × Volume of body
Now, we can solve for the volume of the body:
1.2g/cm^3 × Volume of body = 9.0g/cm^3 × Volume of body
Dividing both sides of the equation by 1.2g/cm^3:
Volume of body = (9.0g/cm^3 / 1.2g/cm^3) × Volume of body
Simplifying:
Volume of body = 7.5 × Volume of body
Now, we can divide both sides of the equation by 7.5:
Volume of body / 7.5 = Volume of body
This is a contradictory statement, which means there is no unique solution. Hence, it is not possible to determine the volume of the solid using the given information.