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In equilibrium, horizontal force of liquid1 is equal and opposite to that of liquid2.
Force of liquid2 per unit length of cylinder= 3dgR2sin(theta)cos(theta) d(theta) = 3dgR2/2 = F1
Force of liquid1 per unit length of cylinder= 2dgR(Rsin(theta)+H – R)cos(theta) d(theta)
= F2 = dgR2 +2dgR(H – R) + dg(H – R)2
F1 = F2 implies H = R(sqrt(3/2))
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