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In general, as objects get larger, mass increases faster than height, because height is a linear, or one dimensional measurement, whereas mass is related to volume, and volume would as a general rule be proportional to the cube of the height. I will add that your question is rather vague. A person who is getting fat, for example, could double in mass without any change in height. An empty box could have something put inside it that would cause it to double in mass without any increase in height. There are many different possible situations involving increased mass, which would have a variety of effects on height.

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Q: How would doubling mass of an object affect its height?
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