Question

An object has density ρ.
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.

Short answer

a) Density will not change.

b) Density will decrease by a factor of 8.

Step-by-step solution

Part(a) Step 1: Given information

Density of object =ρ
All three dimension increased by a factor of 2 without changing the material of which the object is made.

Part(a) Step2: Explanation

The density of an object is defined as

density =Mass/Volume

If material is not changed so as volume increases, mass also increases.

So the density will not change

Part(b) Step 1: Given information

Density of object =ρ
All three dimension increased by a factor of 2 .

Mass is not changing.

Part(b) Step2: Explanation

The density of an object is defined as

density =Mass/Volume

After changing the dimension by 2. The volume will increase by a factor of 8

Assume initial volume = V and Mass = M

then

ρ = M/V .....................................(1)

Once dimension is increased the volume will become 8V

so the density will be

ρ'=M/(8V) .....................................(2)

Substitute M/V =ρ in equation(2), we get,

we get

ρ'=ρ /8

So the density will decrease by a factor of 8