Two objects have masses of #36 MG# and #18 MG#. How much does the gravitational potential energy between the objects change if the distance between them changes from #81 m# to #27 m#?

Answer 1

#\Delta U = U_2 - U_1 = Gm_1m_2(1/d_1-1/d_2)= -1.07\times10^{-21}\quad J#

It is not clear what you mean by MG. It is a strange notation for a mass unit. It could mean Mega Grams which could easily be stated as #1000 \quad kg#. So I assume you mean milli-grams by the symbol MG in solving this problem.
Gravitational Potential Energy: The Gravitational potential energy between two point masses #m_1# and #m_2# separated by a distance #d# is -
#U = -G\frac{m_1m_2}{d}#
The change in gravitational potential energy of the system when the distance changes for #d_1# to #d_2# is :
#\Delta U = U_2 - U_1 = Gm_1m_2(1/d_1-1/d_2)#
#G=6.67\times10^{-11}(Nm^2)/(kg^2); \qquad d_1 = 81\quad m; \qquad d_2=27\quad m;# # m_1 = 36\times10^{-6}\quad kg; \qquad m_2 = 18\times10^{-6}\quad kg #
#\Delta U = -1.07\times10^{-21}\quad J#

Given that in attractive interactions the potential energy decreases if the objects are brought closer together, the negative sign denotes a decrease in potential energy of that magnitude.

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Answer 2

The change in gravitational potential energy between the objects is (2.88 \times 10^{14}) joules.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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