Question

In the figure shown, the heavy cylinder (radius R) reasting on a smooth surface separates two liquids of densities `2rho` and `3rho`. The height h for the equilibrium of cylinder must be

A. `(3R)/2`
B. `Rsqrt(3/2)`
C. `Rsqrt(2)`
D. `Rsqrt(3/4)`

Answer 1

Correct Answer - B

`rhogyds costhetadA`
`intrhogydA`
`=rhogintdA`
`F_(1)=2rgh/2xxhxxl`
`F_(2)=3rhogR/2xxRxxl`
forequilibrium
`2rhogh/2hl = 3rhogR/2Rl`
`h^(2)=3R^(2)/2`
`h=Rsqrt(3/2)`