An object has density rho. a. Suppose each of the object's 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 object's three dimensions is increased by a factor of 2 without changing the object's mass. Will the density change? If so, by what factor? Explain.

a. the density will not change

b. D' = 0.125 D

So, the density will change by a factor of 0.125

Explanation:

a.

Density is the material property and the value of density is constant for all solid materials. So, when the dimensions of the a solid are increased, while the material is same, then the material must be added to the object for increasing its dimensions. So, with the increase in the volume, the mass of the object also increases. And as a result the density of the object remains constant.

Since, here the material remains the same.

Therefore, the density will not change

b.

Density = mass/Volume

D = m/V   equation (1)

Now,

V = LWH   equation (2)

Now, if each dimension increases by a factor of 2, the volume becomes:

V' = (2L)(2W)(2H)

V' = 8 LWH

using equation (2)

V' = 8 V

So, for constant mass, density becomes:

D' = m/V'

D' = m/8V

using equation (1)

D' = D/8

D' = 0.125 D

So, the density will change by a factor of 0.125