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# A particle of mass 3m is located 1.00 m from a particle of ## Problem 9E Chapter 13

University Physics | 13th Edition

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Problem 9E

A particle of mass 3?m is located 1.00 m from a particle of mass ?m?. (a) Where should you put a third mass ?M so that the net gravitational force on ?M due to the two masses is exactly zero? (b) Is the equilibrium of ?M at this point stable or unstable (i) for points along the line connecting ?m and 3 ?m?, and (ii) for points along the line passing through ?M? and perpendicular to the line connecting ?m? and 3 ?m??

Step-by-Step Solution:

Solution 9E Step 1 a) Suppose, the distance between the mass m and M as “x” metres. Then, the gravitational force of attraction between these two masses would be, F = GMm 1 x2 The distance between the masses M and 3m is, (1-x) metres Therefore, the gravitational force acting between these two forces would be, 3GMm F =2 2 (1x) At equilibrium point, both these forces will be equal in magnitude and opposite in direction and we can find out that point. F1= F2 GMm = 3GMm x2 (1x) That is, 12 = 3 2 x (1x) 2 2 That is,(1 x) = 3x 1+x - 2x = 3x 2 That is, 2x + 2x - 1 = 0 Solve for x and we will get the point. 2± 4+8 x = 4 2±2 3 x = 4 x = 1± 3 2 We can take only positive values. x = 1+1.732 = 0.732/2 = 0.366 m 2 The equilibrium point for M is 0.366 m from the mass “m”.

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##### ISBN: 9780321675460

This textbook survival guide was created for the textbook: University Physics, edition: 13. University Physics was written by and is associated to the ISBN: 9780321675460. This full solution covers the following key subjects: line, mass, particle, points, connecting. This expansive textbook survival guide covers 26 chapters, and 2929 solutions. The full step-by-step solution to problem: 9E from chapter: 13 was answered by , our top Physics solution expert on 05/06/17, 06:07PM. The answer to “A particle of mass 3?m is located 1.00 m from a particle of mass ?m?. (a) Where should you put a third mass ?M so that the net gravitational force on ?M due to the two masses is exactly zero? (b) Is the equilibrium of ?M at this point stable or unstable (i) for points along the line connecting ?m and 3 ?m?, and (ii) for points along the line passing through ?M? and perpendicular to the line connecting ?m? and 3 ?m??” is broken down into a number of easy to follow steps, and 83 words. Since the solution to 9E from 13 chapter was answered, more than 704 students have viewed the full step-by-step answer.

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