WEBVTT
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This is Giancoli Answers with Mr. Dychko.
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In the first case, acceleration due
to gravity will be capital *G* times
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some original mass divided by
some original radius squared.
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And then in the second case,
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we have a different mass
and a different radius,
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and we are told that the mass two is
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twice mass one, with
double the mass,
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and the radius in the second case is
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triple the radius in the first case
so 3 times *r 1*.
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So we make substitutions
for each of these
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in the second case
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for acceleration due to gravity.
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So we have capital *G* times
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2 *m 1* instead of *m 2*
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and we have 3 *r 1* instead of *r 2*.
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By the way, I should have a
square there, that's better.
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This 3 on the bottom becomes 9
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because it gets squared
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and so we have two-ninths times
capital *G m 1* over *r 1 squared*
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and this whole thing is the acceleration
due to gravity, in the first case,
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before you doubled the mass
and tripled the radius.
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So that means that
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the acceleration due to gravity
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changes by a factor of two-ninths,
in the second case,
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after you double the mass
and triple the radius.