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.