Momentum and CollisionHard

Question

A small uniform tube is bent into a circular tube of radius R and kept in the vertical plane. Equal volumes of two liquids of densities ρ and s (ρ > σ) fill half of the tube as shown. θ is the angle which the radius passing through the interface makes with the vertical. The value of θ is : -

Options

A.θ = tan-1
B.θ = tan-1
C.θ = tan-1
D.θ = tan-1

Solution


Given ⎳COD = Q
G1 & G2 be the center of gravities of two liquids, then
⎳AOC = 90o = COB
⎳AOG1 = 45o
⎳G1OD = 45o-
⎳G2OD = 45 + 
Net torque about point O is zero
⇒ rm1g sin (45o- θ) = rm2gsin(45 + θ)
svsin (45 - θ) = σvsin (45 - θ)



= tan θ
θ = tan-1


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