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# two similar helium filled spherical balloon tied to weight 5g weight with strings and each carrying a electric charge q floats in equilibrium as shown in figure. find the magnitude of q assuming that the charge on each balloon as if it were concentrated at its centre. find the volume of each balloon [neglect the weight of unfilled balloon and assume that the density of air is 0.00129gm/cc and density of helium inside the balloon is 0.0002 gm/cc]

ALWINDER SINGH
13 Points
2 years ago
Here,@ has been used for thita

Solution:
2Tcos@=(mg)=5*10^-3*10
(WKT,9cos@=B/H
B2=H2-P2
=1-(0.3)^2
Root of 1-(0.3)^2
=0.9(aprrox))
.'. 2T(0.9)=5*10^-3*10
T=5*10^-2/2*0.9
T=5*10^-2/1.8-------------(1)
lly,Tcos@=5*10^-2/2-----------(2)
Also,Tsin@=5*10^-2*0.3/1.8*1----------(bcz sin@=0.3/1)
Tsin@=5*10^-2/6-------------(3)

Now Tsin@=F(electrical)
5*10^-2/6=9*10^9*q^2/(6*10^-1)^2
q^2=5*10^-2*6*6*10^-2/6*9*10^9
q^2=10/3*10^-13
q^2=10*10*10^-14/3-----------(for math convinence)
q=17/3*10-7
q=5.5*10^-7(approx)--------(ans 1)

Now,
Tcos@=F(buoyancy)
Tcos@=V(rho-sigma)g-----------(archimede principle)
5*10^-2=V(1.29-0.2)*10--------------(in kg/m^3 and g=10m/s^2)
So V=5*10^-2/2*11
HenceV=2.3*10-3m^3 (ans 2)