Question

Two balls A and B of same mass (M) and charges Q, -Q are suspended by two strings of same length from two different suspension points $S_1$ and $S_2$ if $S_1{S}_2$ =3x and AB = x then show that -

• A. tension in the string is $T=\frac{Q^{2}L}{4\pi {ϵ}_0{x}^3}$
• B. tan $\theta =\frac{Q^{2}L}{4\pi {ϵ}_0{x}^{2}Mg}$
• C. tan $\theta =\frac{QL}{4\pi {ϵ}_{0}xMg}$
• D. tan $\theta =\frac{QL}{4\pi {ϵ}_0{x}^3}$

Answer 1

The correct option is B tan $\theta =\frac{Q^{2}L}{4\pi {ϵ}_0{x}^{2}Mg}$

$FromthefigurewehaveT\cos \theta =MgT\sin \theta =\frac{Q^2}{4\pi {\epsilon }_0{x}^2}And2Lsin\theta =2x\Rightarrow x=Lsin\theta Puttingthevalueofsin\theta wegetT=\frac{Q^{2}L}{4\pi {\epsilon }_0{x}^3}ThereforeoptionAtan\theta =\frac{Q^2}{4\pi {\epsilon }_0{x}^{2}Mg}$