Q) Four particles having masses m , 2m , 3m and 4m are placed at the four corners of a square of edge a . Find the gravitational force acting on a particle of mass m placed at the centre .
Ans)
(m)A.....................B(2m)
.
.
.
. (m)O
.
.(4m)C...................D(3m)
Force at cente due to masses at A and D = F1
where F1= 2G(3m-m)m/a2 = 4Gm2 / a2 along OD
Similarly due to masses at C and B is = F2
or F2 = 4Gm2 / a2 along OC
Thus resultant of F1 and F2 which are equal perpendicular to each other = F = 
{(F
1)
2+ (F
2)
2} = 4(
2)Gm
2 / a
2
Moderation Team
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