Question

An object has density.

A) Suppose each of the objects three dimensions is increased by a factor of 2 without changing the material of which the object is made. Will the density change? If so, by what factor? Explain.

B) Suppose each of the objects three dimensions is increased by a factor of 2 without changing the objects mass. Will the density change? If so, by what factor? Explain.

Answer 1

Part A.

Density is an intensive property of objects, So it does not depends on the shape of object, it always remains constant.

So since each material have a constant density, So in this case since we are not changing the material than density of object won't change.

Part B.

Now in this case since mass is constant and it's volume is increased, So using the relation

Mass = Density*Volume

Density = Mass/Volume

Since mass is constant, and each of the three dimensions are increased by a factor of 2, So it's new volume will be increased by a factor of 8, which means it's density will change, which is inversely proportional to the Volume, will decreased by a factor of 8.

Volume of any object = C*side*side*side, here C is constant term

So new Volume = C*(2*side)*(2*side)*(2*side) = 8*side^3

Please Upvote.