There are two cylinder shaped wooden billets, each having a mass of mass `45kg`, in a vertical wall sewage, which contains water in it. the two billets have the same size and the same material, they touch each other and the walls of the sewage. One of them is totally under the water, whilst only half of the other one is immersed into the water. Friction is negligible everywhere. (density of water is `1000kg//m^(3)` and `g=10m//s^(2)`). Choose the correct option(s)

Options

A. Density of the wood is `750 kg//m^(3)`
B. Density of the wood is `800kg//m^(3)`
C. The forces exerted by the billets on the vertical walls is `260N` approximately
D. The forces exerted by the billets on the vertical walls is `320N` approximately

Answer

A, C

Explanation

`2mg=F_(B_(1))+F_(B_(2))`
`impliesrho_("wood")=3/4rho_("water")=750kg//m^(3)`
Taking torque about `O_(1)`
`NxxR=(mg-F_(B2))xx2Rcos30^(@)`
`implies-45xx10xx1/3xx1.732=259.8~~260N`