A wooden cylinder of diameter 4 r, height H and density `rho//3` is kept on a hole of diameter 2 r of a tank, filled with water of density `rho` as shown in the

The block in the above question is maintained by external means and the level of liquid is lowered. The height `h_(2)` when this external force reduces to zero is

Answer

`h_(1)=(2(3+pi))/(15pi)=0.26;h_(2)=(3+pi)/(10pi)=0.195`

Explanation

To open plug
`B=mg+` force of pressure of water on plug
`(h=10) pi xx (10)^(2) xx g = 3000g + (hxx1xxg) xx pi xx (5)^(2)`
`100pi (h-10) = 3000+25pih`
`75pih = 3000+1000pi`
`h=(3000+1000pi)/(75pi)cm implies h = (30+10pi)/(75pi)m`
`h=(6+2pi)/(15pi)m " "implies h=(2(3+pi))/(15pi)`
To close plug
`mg = B`
`3000g(h-10) pi (10)^(2) xx g`
`100(h-10)pi=3000`
`pih-10pi=30`
`h=(30+10pi)/(pi)m" "implies " "h=(3+pi)/(10pi)m`