Question

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

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

Answer 1

Answer: (B)

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