Question

If the volume of an object were to double, with no change in mass, its density would? a) Halve b) Double c) Be the same d) None of these

Answer 1

`"a)"` `"Halve"`

Explanation:

The formula for density is `"density" = frac("mass")("volume")`.

We need to double the volume, i.e. multiply it by `2`.

But in order to multiply one side of the equation by a number, the same has to be done to the other side.

Multiplying the volume by `2` is the same as multiplying the fraction `frac("mass")("volume")` by `frac(1)(2)`.

So let's multiply both sides of the equation by `frac(1)(2)`:

`Rightarrow frac(1)(2) times "density" = frac(1)(2) times frac("mass")("volume")`

`Rightarrow frac("density")(2) = frac("mass")(2 times "volume")`

Therefore, doubling the volume results in the density being halved.