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Question

Solve the integral I=RGMmx2dx


A

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B

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C

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D

- GMm ln(R)

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Solution

The correct option is A


I=RGMmx2dx=GMmRdxx2=GMm[1x]R

=GMm1R+1=GMmR

This expression represents the gravitational potential energy which is obtained by integrating GMm/x2 between the limits infinity () and radius of the earth (R).


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