In the figure, two spheres of mass m = 9.18 kg. and a third sphere of mass M for

Question

In the figure, two spheres of mass m = 9.18 kg. and a third sphere of mass M form an equilateral triangle, and a fourth sphere of mass m4 is at the center of the triangle. The net gravitational force on that central sphere from the three other spheres is zero. (a) What is the value of mass M? (b) If we double the value of m4, what then is the magnitude of the net gravitational force on the central sphere? The answer to part B is 0. I dont get Part A - Please provide the numerical answer to part A.

Explanation / Answer

a)By symmetry, if all 3 spheres pull the center sphere with the same force then the forces will cancel out.

M = 9.18kg

Alternately, the net downward force due to both m = 2xGm4mcos60/r^2 = Gmm4/r^2

This should be balanced by M. Force by M = GMm4/r^2

On equating we get M = m = 9.18kg

b) If the net force is 0, for any value of m4 all forces will increase proportionately and the net force will still remain 0.

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.