Three indentical spherical particles of mass m eachlocated at the corners of an

Question

Three indentical spherical particles of mass m eachlocated at the corners of an equilateral triangle with edge lenghtr ( each sphere is centered at each corner). Show the magnitude ofthe net gravitional force acting on any one of the other twoparticles is given by:                                      Fg=3Gm2/r2 Three indentical spherical particles of mass m eachlocated at the corners of an equilateral triangle with edge lenghtr ( each sphere is centered at each corner). Show the magnitude ofthe net gravitional force acting on any one of the other twoparticles is given by:                                      Fg=3Gm2/r2

Explanation / Answer

the force acting between first and third spheres is F1= (G * m * m/r2) = (G *m2/r2) ---------(1) the force acting between the second and third spheres is F2= (G * m * m/r2) = (G *m2/r2) ---------(2) the resultant force acting on the third sphere is F = (Fx2+Fy2)1/2 ----------(3) Fx = F1x + F2x =F1 * cos1 + F2 *cos2 ----------(4) and Fy= F1y + F2y =F2 * sin1 + F2 *sin2 -----------(5) 1= 2= 60o substituting the above values in equations (3) and (4) weget Fx = F1 * cos(60o) +F2 * cos(60o) = (1/2) * (F1 +F2) and Fy= F1 * sin(60o) +F2 * sin(60o) = 0.866 * (F1 +F2) substituting the above values in equation (3) we get theresultant force. substituting the above values in equations (3) and (4) weget Fx = F1 * cos(60o) +F2 * cos(60o) = (1/2) * (F1 +F2) and Fy= F1 * sin(60o) +F2 * sin(60o) = 0.866 * (F1 +F2) substituting the above values in equation (3) we get theresultant force.

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