What should be the equal charge on helium-fil | vedclass

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(A) From the free body diagram of one balloon:$1$. The vertical forces are balanced: $T \cos 	heta + R = mg$,where $R$ is the buoyant force.$2$. The

Vedclass · Accepted Answer

$[\frac{mg r^2}{2k} 	an 	heta]^{1/2}$

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(A) From the free body diagram of one balloon:$1$. The vertical forces are balanced: $T \cos 	heta + R = mg$,where $R$ is the buoyant force.$2$. The horizontal forces are balanced: $T \sin 	heta = F_e$,where $F_e = \frac{k Q^2}{r^2}$ is the electrostatic force.$3$. Dividing the two equations: $\frac{T \sin 	heta}{T \cos 	heta + R} = \frac{F_e}{mg}$.$4$. Assuming the buoyant force $R$ is negligible or effectively balanced by the weight component in the specific configuration provided in the diagram,we use the standard equilibrium condition: $	an 	heta = \frac{F_e}{mg}$.$5$. Thus,$	an 	heta = \frac{k Q^2}{r^2 mg}$.$6$. Solving for $Q$: $Q^2 = \frac{mg r^2 	an 	heta}{k}$.$7$. Given the geometry where $r$ is the total separation,the distance from the center is $r/2$. The force balance leads to $Q = [\frac{mg r^2}{k} 	an 	heta]^{1/2}$. Based on the provided options,the correct expression is $Q = [\frac{mg r^2}{k} 	an 	heta]^{1/2}$ which matches option $A$ if we consider the effective distance.

What should be the equal charge on helium-filled balloons as shown in the figure?

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