Question

Two similar helium filled balloons, each carrying charge Q, are tied to a 30 g weight and are floating at equilibrium as shown in the figure. The charge Q on each balloon must be:

• A. $14.14\mu C$
• B. $56.56\mu C$
• C. $21.2\mu C$
• D. $7.07\mu C$

Answer 1

The correct option is C $21.2\mu C$

At equilibrium of the System,

From FBD of mass:

$mg=Tcos\theta +Tcos\theta =2Tcos\theta$..................................(i)

From FBD of balloon:

$F_E$:Electrostatic repulsive force

$F_E=\frac{1}{4\pi {\epsilon }_0}.\frac{Q^2}{d^2}=\frac{1}{4\pi {\epsilon }_0}.\frac{Q^2}{36}$

$Tsin\theta =F_E$.........(2)

$\left(2\right)÷\left(1\right),\frac{1}{2}tan\theta =\frac{F_E}{mg}=\frac{3}{8}\Rightarrow F_E=\frac{3}{8}mg$
$(\because tan\theta =\frac{3}{4})$

$\therefore \frac{1}{4\pi {\epsilon }_0}.\frac{Q^2}{36}=\frac{3}{8}\times 30\times {10}^{-3}\times 10$

$Q^2=4.5\times {10}^{-10}$

$Q=21.2\mu C$