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

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Answer 1 · 2017-08-27T18:55:20

$"a)"$ $"Halve"$

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.