Question

Find the height of the water level $h_2$ (in situation 2), for which the block remains in its original position without the application of any external force

• A. $h/3$
• B. $4h/9$
• C. $2h/3$
• D. $h$

Answer 1

Answer: (B)

$4h/9$

Area of the hole $=\pi {\left(2r\right)}^2=4\pi r^2$
Area of the block $=\pi {\left(4r\right)}^2=16\pi r^2$
Area of the lower face in contact with liquid $=16\pi r^2-4\pi r^2=12\pi r^2$
The block will not move if the upthrust $U$ equals the weight $W$ of the block
$\Rightarrow \rho g{h}_2\times 12\pi r^2=\frac{\rho }{3}\times (h\times 16\pi r^2)\times g\Rightarrow h_2=\frac{4h}{9}$