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 center.

Answer

A, B, D

Explanation

To calculate the gravitatioN/Al force on m due to other force

here `r=sqrt((a/2)^2+(a/2)^2)=a/sqrt2`
`vecF_(OB)=(G.m.2m)/r^2`
`vecF_(OC)=(G.m.3m)/r^2`
and `vecF_(OD)=(G.m.4m)/r^2`
Resultant force `=vecF_(OA)+vecF_(OB)+vecF_(OC)+vecF_(OD)`
`=(2Gmm)/a^2[-veci/sqrt2+vecj/sqrt2]+(4Gmm)/a^2[veci/sqrt2+vecj/sqrt/2]
`=(6Gmm)/a^2[veci/sqrt2-vecj/sqrt2]+(8Gmm)/a^2[(-veci)/sqrt2-(-vecj)/sqrt2]`
`F=(4sqrt2Gm^2)/a^2