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Comparing Coulomb's Constant and Gravitational Constant

Three point c...

Question

Three point charges $q_{1}, q_{2}$ and $q_{3}$ are taken such that when $q_{1}$ and $q_{2}$ are placed close together to form a single point charge, the force on $q_{3}$ at distance $L$ from this combination is a repulsion of $2$ unit magnitude. When $q_{2}$ and $q_{3}$ are combined, the force on $q_{1}$ , from same distance $L$ is of magnitude $4$ unit and is attractive. Also $q_{3}$ and $q_{1}$ combining exert $6$ a force of magnitude $18$ unit attractive on $q_{2}$ from same distance $L$ , Algebraic ratio of charges $q_{1}, q_{2}$ and $q_{3}$ is:

1 : 2 : 3

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2 : - 3 : 4

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4 : - 3 : 1

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4 : - 3 : 2

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Solution

The correct option is A $1 : 2 : 3$
$\frac{q_{3} (q_{1} + q_{2})}{L^{2}} = 2$
$\frac{q_{1} (q_{2} + q_{3})}{L} = - 4$
$\frac{q_{2} (q_{1} + q_{3})}{L^{2}} = 18$
$\frac{K_{1} (K_{1} + 1)}{K_{1} (1 + K_{2})} = \frac{1}{9}$
$\frac{K_{1} + K_{2}}{K_{2} (K_{1} + 1)} = - 2$
$K_{2} = (\frac{K_{1}}{8 K_{1} + 9}) = 2$
$q_{1} : q_{2} : q_{3} = 1 : \frac{- 6}{5} : 2$

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The correct option is A 1:2:3q3(q1+q2)L2=2q1(q2+q3)L=−4q2(q1+q3)L2=18K1(K1+1)K1(1+K2)=19K1+K2K2(K1+1)=−2K2=(K18K1+9)=2q1:q2:q3=1:−65:2