21 Three particles each of mass m are placed on the three corners of a square of side L - Physics -

Question

21 Three particles each of mass m are placed on the three corners
of a square of side L m Calculate the fourth particle of mass m
placed at corner D
Ans is (Gm^2/L^2 ) (√2 + ½)along BD

Vara · Accepted Answer

Dear
Student,
Please find below the solution
to the asked query:
Newton's universal law of gravitation:F=Gm1m2r2Force on mass at D due to mass at A:F1=Gm2L2Force on mass at D due to mass at C:F2=Gm2L2Force on mass at D due to mass at B:F3=Gm22L2=Gm22L2Net force at D due to A and C:F4=F12+F22     =2Gm2L2Net force at D:Fnet=F4+F3        =2Gm2L2+Gm22L2        =Gm2L22+12Direction: along the diagonal BD
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21. Three particles each of mass m are placed on the three corners of a square of side L m. Calculate the fourth particle of mass m placed at corner D. Ans is (Gm^2/L^2 ) (√2 + ½)along BD

21. Three particles each of mass m are placed on the three corners of a square of side L m. Calculate the fourth particle of mass m placed at corner D.
Ans is (Gm^2/L^2 ) (√2 + ½)along BD