Question

Two identical helium filled balloon $A$ and $B$m fastened to a weight of $5g$ by threads floats in equilibrium as shown in fig. Calculate the charge on each balloons, assuming that they carry equal charges

Answer 1

$OC=\sqrt{O{A}^2-A{C}^2}$

= $\sqrt{(1{)}^2-(0.3{)}^2}$ = 0.954

As the balloons float in equilibrium.

Using triangle law of vectors, We get -

$\frac{F}{AC}=\frac{w}{OC}$

where, w = upthrust acting on each ballon.

As W = $w+w$

$w=\frac{W}{2}$

F = $\frac{AC}{OC}\times \frac{W}{2}$

$\frac{q\times q}{4\pi {ϵ}_0(AB{)}^2}$ = $\frac{AC}{OC}\times \frac{mg}{2}$

$q^2=\frac{(0.6{)}^2\times (0.3)\times (5\times {10}^{-3}\times 9.8)}{9\times {10}^9\times 0.954\times 2}$

$q^2=\frac{0.36\times 0.30\times 49}{9\times 0.954\times 2}\times {10}^{-7}C$

q = ${}_{-}^{+}5.6\times {10}^{-7}C$