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

If level of liquid starts decreasing slowly, when the level of liquid is at a height `h_(1)` above the cylinder, the block just start moving up. Then the value of `h_(1)` is

Options

A. `(2h)/(3)`
B. `(5h)/(4)`
C. `(5h)/(3)`
D. `(5h)/(2)`

Answer

C

Explanation

Area of hole `=pi(2r)^(2)=4pir^(2)=A`
Area of block `=pi(4pi)^(2)=16pir^(2)=4A`
Area of lower face of block in contact with liquid `=4A-A=3A`
For block to just rise
upward thrust = weight
`(h_(1)+h)rhogxx3A-h_(1)rhogxx4A=4Ah(rho)/(3)g`
`3(h_(1)+h)-4h_(1)=(4h)/(3)" "implies" "h_(1)=3h-(4h)/(3)implies h_(1)=(5h)/(3)`