Question

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

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

Answer 1

Answer: (B)

From equilibrium of charge $q$,
$k\left[\frac{2q^2}{d^2}+\frac{4q^2}{4d^2}\right]=T_{AB}\Rightarrow T_{AB}=\frac{3k{q}^2}{d^2}$
From equilibrium of charge $4q$,
$k\left[\frac{8q^2}{d^2}+\frac{4q^2}{4d^2}\right]=T_{BC}\Rightarrow T_{BC}=\frac{9k{q}^2}{d^2}$
Thus, $\frac{T_{AB}}{T_{BC}}=\frac{1}{3}$