A solid weighing 277.5g in air and 212.5g is totally immersed in a liquid of density 0.9g/cm^3 . Calculate the density of the solid.
I think the student means it weighs 277.5 g in air and 212.5 g when immersed in the liquid of density 0.9 g/cc.
So liquid displaced by the object is 277.5 - 212.5 = 65 g
Volume of liquid displaced = mass/density = 65 g/0.9 g/cc = 72.22 cc = volume of the solid.
density of the solid = mass/volume = 277.5/72.22 = ?
The previous answer by me.
eh?
how can it weigh "277.5g in air and 212.5g" ??
To calculate the density of the solid, we need to use the principle of buoyancy. The buoyant force acting on an object immersed in a fluid is equal to the weight of the fluid displaced by the object. In other words, the weight of the solid when immersed in the liquid will be less than its weight in air due to the buoyant force.
Let's begin by calculating the weight of the solid in air (W_air):
W_air = 277.5g
Now, let's calculate the weight of the solid when immersed in the liquid (W_liquid). The buoyant force acting on the solid is equal to the weight of the liquid displaced. We can calculate the volume of the solid using the Archimedes' principle.
Archimedes' principle states that the buoyant force experienced by an object immersed in a fluid is equal to the weight of the fluid it displaces. Mathematically, it can be written as:
Buoyant force = Weight of the fluid displaced
The weight of the fluid displaced can be calculated as follows:
Weight of the fluid displaced = Volume of the solid × Density of the liquid × acceleration due to gravity
We need to rearrange this formula to solve for the volume of the solid:
Volume of the solid = Weight of the fluid displaced / (Density of the liquid × acceleration due to gravity)
Given that the density of the liquid is 0.9 g/cm^3, we convert the weight of the fluid displaced and the weight of the solid to the corresponding units.
W_liquid = Weight of the fluid displaced = (W_air - W_liquid) = (277.5g - 212.5g) = 65g
Now, the volume of the solid can be calculated as:
Volume of the solid = 65g / (0.9 g/cm^3 × 9.8 m/s^2)
(Note: We use 9.8 m/s^2 for the acceleration due to gravity)
Next, we need to find the density of the solid. The density (D) is defined as the mass (m) of an object divided by its volume (V):
Density of the solid = mass of the solid / volume of the solid = (277.5g / Volume of the solid)
Now, let's substitute the values into the above equation to find the density of the solid.
Density of the solid = (277.5g / (65g / (0.9 g/cm^3 × 9.8 m/s^2)))
After performing the calculations, you will get the density of the solid.