Question

Archimedes' Principle: Based on free body diagrams and the definition of density, derive the formula used to calculate the density of irregular objects

Answer 1

According to the Archimedes principle, the fluid will exert an upward force on the object equal to the weight of the fluid displaced by that object.

Let V be the volume of the body of mass m.

V' be the volume displaced by the body.

is the density of the body and be the density of the fluid.

Since the fluid is applying an upward force on the body, its weight will decrease.

let W be the actual weight and W' be the apparent weight of the body.

Where m'g is the weight of the fluid displaced by the body.

If the object is completely immersed in the fluid then V' = V,

Now we can measure the actual weight and the apparent weight of the body by using the spring balance. Provided the density of the fluid, the density of the object can be calculated.

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