Three balls, with masses of 4 m , 2 m , and m , are equally spaced along a line.

Question

Three balls, with masses of 4m, 2m, and m, are equally spaced along a line. The spacing between neighboring balls is r. We can arrange the balls in three different ways, as shown in the figure. In each case, the balls are in an isolated region of space very far from anything else. Treat the balls as point objects.

(a) Rank the arrangements according to their gravitational potential energy, from most positive to most negative. See if you can do this without explicitly calculating the potential energy in each case. (Use only ">" or "=" symbols. Do not include any parentheses around the letters or symbols.)


(b) Using m is 7.00 kg and r is 60.0 cm, calculate the gravitational potential energy in case 1 above.

Explanation / Answer

Here ,

as gravitational potential of two masses is given as

U = - G * m1 * m2 /d

where d is the distance between them

for 1

U1 = - G * (4m * 2m/r + 2m * m/r + 4m * m/(2r))

U1 = - 12 * G m^2/r

for 2

U2 = - G * (2 m * 4m /r + 4m * m/r + 2m * m/2r)

U2 = --3 * G m^2/r

for 3

U3 = - G * (4 m * m /r + 2m * m /r + 4m * 2m /2r)

U3 = -10 * G*m^2/r

the order of the potential energy is

3 > 1 > 1

b)

for the 1 ,

U1 = - 12 * G m^2/r

gravitational potential energy = -12 * 6.673 *10^-11 * 7^2/.60

gravitational potential energy = -6.54 *10^-8 J

the gravitational potential energy of system 1 is -6.54 *10^-8 J

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