Four objects with different masses, m1 < m2 < m3 < m4 are made of the same mater

Question

Four objects with different masses, m1 < m2 < m3 < m4 are made of the same material (so they have the same density). The masses are m1 = 0.5 kg, m2 = 2 m1, m3 = 2 m2, and m4 = 2 m3. The four objects float in water. Let V1 = volume of object 1, V2 = volume of object 2, V3 = volume of object 3, and V4 = volume of object 4. Ranks the objects from largest to smallest by the fraction of the object's volume that is submerged when the object floats in water.

a) object 1 = object 2 = object 3 = object 4

b) object 1 > object 3 > object 2 > object 4

c) object 4 > object 3 > object 2 > object 1

d) object 1 > object 2 > object 3 > object 4

The correct answer is a). Please show step by step solutions and clearly identify the equations used/with explanations.

Explanation / Answer

Here ,

let the density of object is p

let the fraction of object inside water is k

volume of object is V

Now , using archimedes principle

weight of water displaced = weight of object

V * p * g = k * pwater * V * g

k = p/pwater

hence , the fraction of the object inside water is dependent only on the density of object and desnity of water.

hence , fraction of object value submerged in water will be same for all objects as the density is same for all objects

hence ,

the correct choice is a) object 1 = object 2 = object 3 = object 4

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