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

Options

A. `4 H//9`
B. `5 H//9`
C. remains same
D. `2 H//3`

Answer

A

Explanation

as the cylinder is in equilibrium, so

`P_(0)A_(1) + (rho)/(3) g HA_(1) =P_(0)A_(1) + rho g h_(2)A_(3)`
On solving, `h_(2) =4H//9`