Calculatingthe resultant gravitational force on spherical objects

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The discussion focuses on calculating the resultant gravitational force on spherical objects, specifically addressing the direction of force components. It notes that the positive x-axis is oriented to the right, while the x-component of the force is directed to the left. A key point raised is the importance of correctly assigning negative values to force components when they act in the opposite direction of the defined axis. This correction is essential for accurate calculations in gravitational force analysis. Properly accounting for the direction of forces ensures accurate results in physics problems involving spherical objects.
naushaan
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Homework Statement
Hi guys, I'm stuck on this homework question: Three uniform spheres of masses m1 = 2.50 kg, m2 = 4.00 kg, and m3 = 7.50 kg are placed at the corners of a right triangle (see figure below). Calculate the resultant gravitational force on the object of mass m2, assuming the spheres are isolated from the rest of the Universe. So I got the 'j' part correct, but for the 'i' part it's telling me the magnitude is correct but the direction is not. I'm confused as to what this means.
Relevant Equations
F=GMm/r^2
1583810276465.png


1583810347552.png
 
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It looks like the positive x-axis points to the right. The x-component of the force points to the left. So ...
 
i forgot to make it a negative! thank you for your help
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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