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Three mass points each of mass m are pla...

Three mass points each of mass m are placed at the vertices of an equilateral tringale of side l. What is the gravitational field and potential due to three masses at the centroid of the triangle ?

Text Solution

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`E_1=(Gm)/((OA)^2),E_3=(Gm)/((OC)^2)`
From `triangleODBcos 30^@=(BD)/(OB)=(1//2)/(OB)`
`OB=(1//2)/(cos 30^@)=(1//2)/(sqrt3//2)=1//sqrt3`
Gravitational field at O due m at, A B and C is say `vecE_1,vecE_2,vecE_3`
`vecE` is equal and opposite to `vecE_1` `therefore` Net gravitational field
As gravitational potential is scalar `V=V_1+V_2+V_3=(Gm)/(OA)-(Gm)/(OB)-(Gm)/(OC)`
`V=(3GM)/(1//sqrt3)=-3sqrt3(Gm)/1`
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