Calculate, the gravitational field at point O due to three massesm_(1),m_(2) and m_(3)whose positions are given by the following figure. If the masses m_(1) and m_(2)are equal what is the change in gravitational field at the point O?

Calculate, the gravitational field at point O due to three massesm_(1)

1.	Calculate, the gravitational field at point O due to three massesm_(1),m_(2) and m_(3)whose positions are given by the following figure. If the masses m_(1) and m_(2)are equal what is the change in gravitational field at the point O?
Answer» SOLUTION :Gravitationalfielddue to `m_(1)`at a point.O . is `vec(E)_(1) = (Gm_(1))/(a^(2)) hat(i)` Gravitational fielddue to `.m_(1)`at a point.O. is `vec(E)_(2) = - (Gm_(2))/(a^(2)) hat(i)` (Negativesignindicatesfieldacting along negativex DIRECTION ) Gravitational FIELD dueto `m_(3`at a point . O .is `vec(E)_(3) = (Gm_(3))/(a^(2)) hat(j)` `vec(E) = vec(E)_(1)+vec(E)_(2) +vec(E)_(3) = (Gm_(1))/(a^(2))hat(i)- (Gm_(2))/(a^(2)) hat(i) +(Gm_(3))/(a^(2)) hat(j)` `vec(E) = G/(a^(2)) [ (m_(1)-m_(2))hat(i) +m_(3)hat(j) ] ` If the MASSES `m_(1) =m_(2) , ` then `vec(E) = (Gm_(3))/(a^(2)) hat(j)`