Question

Two similar balloons filled with helium gas are tied to $L$ metre long strings. A body of mass $m$ is tied to another ends of the strings. The balloons float in air at distance $r$. If the amount of charge on the balloons is same, then the magnitude of charge on each balloon will be

• A. ${\left[\frac{mg{r}^2}{2k}\tan \theta \right]}^{1/2}$
• B. ${\left[\frac{2k}{mg{r}^2}\tan \theta \right]}^{1/2}$
• C. ${\left[\frac{mgr}{2k}\cot \theta \right]}^{1/2}$
• D. ${\left[\frac{2k}{mgr}\tan \theta \right]}^{1/2}$

Answer 1

Answer: (A)

In equilibrium,
$2R=mg........(i)$
$F_e=T\sin \theta ........(ii)$
$R=T\cos \theta$ ......... (iii)
From equations (i) and (iii),

$2T\cos \theta =mg\dots$(iv)
Dividing equation (ii) by equation (iv),
$\frac{1}{2}\tan \theta =\frac{F_e}{mg}$
$\Rightarrow \frac{1}{2}\tan \theta =\frac{k\frac{Q^2}{r^2}}{mg}$
$\Rightarrow \theta ={\left(\frac{mg{r}^2}{2k}\tan \theta \right)}^{1/2}$