Explanation The formula for gravitational potential energy is, U = − G m 1 m 2 r J (1) Here U is gravitational potential energy G is universal gravitational constant m 1 is mass of object one m 2 is mass of object two r is the distance between the two objects J is joule Substitute m for m 1 , 2 m for m 2 and d for r in equation (1). U A1 = − G m ( 2 m ) d (2) Here, U A1 is first set of potential energy in system A. Substitute m for m 1 , 2 m for m 2 and 2 d for r in equation (1). U A2 = − G m ( 2 m ) 2 d (3) Here, U A2 is second set of potential energy in system A. Substitute 2 m for m 1 , 2 m for m 2 and d for r in equation (1). U A3 = − G 2 m ( 2 m ) d (4) Here, U A3 is third set of potential energy in system A. For system A, total gravitational potential energy from equation (2) , (3) and (4) is, U A = − G m ( 2 m ) d − G m ( 2 m ) 2 d − G ( 2 m ) ( 2 m ) d U A = − 7 G m 2 d (5) Substitute m for m 1 , 2 m for m 2 and d for r in equation (1)

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Chapter 12.4, Problem 4EYU

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Whether the total gravitational potential energy of system A is greater than, less than or equal to that of system B.

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Chapter 12.3, Problem 3EYU

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Whether the total gravitational potential energy of system A is greater than, less than or equal to that of system B.

Solution Summary: The author explains that the total gravitational potential energy of system A is less than that of System B.

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Whether the total gravitational potential energy of system A is greater than, less than or equal to that of system B.

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Chapter 12 Solutions