In Fig. 13-25, three particles are fixed in place. The mass of B is greater than the mass of C. Can a fourth particle (particle D) be placed somewhere so that the net gravitational force on particle A from particles B, C, and D is zero? If so, in which quadrant should it be placed and which axis should it be near?

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Answers:
A) There is no place to put D to make this possible.
B) Yes; put D in the quadrant with x > 0 and y > 0, closer to the x axis.
C) Yes; put D in the quadrant with x > 0 and y > 0, closer to the y axis.
D) Yes; put D in the quadrant with x > 0 and y < 0, closer to the x axis.
E) Yes; put D in the quadrant with x > 0 and y < 0, closer to the y axis.
F) Yes; put D in the quadrant with x < 0 and y < 0, closer to the x axis.
G) Yes; put D in the quadrant with x < 0 and y < 0, closer to the y axis.
H) Yes; put D in the quadrant with x < 0 and y > 0, closer to the x axis.
I) Yes; put D in the quadrant with x < 0 and y > 0, closer to the y axis.

Answer is I

To determine if a fourth particle (particle D) can be placed so that the net gravitational force on particle A from particles B, C, and D is zero, we need to analyze the given scenario.

In Fig. 13-25, three particles (B, C, and D) are fixed in place, and it is mentioned that the mass of B is greater than the mass of C.

To balance out the gravitational forces on particle A, particle D must be placed in a specific position. If we consider the gravitational forces from particles B, C, and D acting on particle A, the force from particle B will be in the opposite direction than the combined force from particles C and D.

Since the mass of B is greater than C, the gravitational force from B will be larger than the combined force from C and D.

To nullify the net gravitational force on particle A, particle D must be placed in a position such that the gravitational force from D cancels out the combined gravitational force from C and D.

Considering the possible positions in terms of quadrants and axes, the only option that satisfies this condition is:
B) Yes; put D in the quadrant with x > 0 and y > 0, closer to the x-axis.

Thus, particle D needs to be placed in the quadrant with positive x and positive y coordinates, closer to the x-axis, in order to achieve a net gravitational force of zero on particle A.

To determine whether a fourth particle (particle D) can be placed to make the net gravitational force on particle A zero, we need to analyze the situation and understand the conditions required for this to happen.

In this case, we have three fixed particles: A, B, and C, with the mass of B being greater than the mass of C.

To make the net gravitational force on particle A zero, we need the gravitational forces from particles B, C, and D to cancel each other out. This means that the gravitational forces must have certain magnitudes and directions.

Since the mass of B is greater than the mass of C, the gravitational force from particle B on particle A will be stronger than the gravitational force from particle C. Therefore, we can conclude that the direction of the net gravitational force will be opposite to the direction of the gravitational force from particle B.

To counterbalance the gravitational force from particle B, particle D needs to be placed in a location where its gravitational force on particle A is equal in magnitude but opposite in direction to the gravitational force from particle B. This way, the forces will cancel each other out, resulting in a net gravitational force of zero.

From the given answer choices, one option stands out as a possibility: "Yes; put D in the quadrant with x > 0 and y > 0, closer to the x axis." This answer suggests placing particle D in the top right quadrant of the coordinate system, closer to the x-axis. This placement can potentially create a gravitational force that counteracts the force from particle B.

Therefore, the correct answer is B) Yes; put D in the quadrant with x > 0 and y > 0, closer to the x-axis.