Three charges `+q, +2q` and `4q` are connected by strings as shown in the figure.What is ratio of tensions in the strings `AB` and `BC`

Options

A. `1:2`
B. `1:3`
C. `2:1`
D. `3:1`

Answer

B

Explanation

From equilibrium of charge `q`,
`k[(2q^(2))/(a^(2))+(4q^(2))/(4d^(2))]= T_(AB)implies T_(AB)= (3kq^(2))/(d^(2))`
From equilibrium of charge `4q`,
`k[(8q^(2))/(d^(2))+(4q^(2))/(4d^(2))]=T_(BC)implies T_(BC)= (9kq^(2))/(d^(2))` Thus `(T_(AB))/(T_(BC))= (1)/(3)`