Question

Find the minimum value of height $h_1$ (in situation 1) for which the block just starts to move up?

• A. $2h/3$
• B. $5h/4$
• C. $5h/3$
• D. $5h/2$

Answer 1

The correct option is C $5h/3$

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 $=16\pi r^2-4\pi r^2=12\pi r^2$

When the block starts rising

upthrust = weight

$\because \text{upthrust}=F_1-F_2=\rho g(h_1+h)\times 12\pi r^2-\rho g{h}_1\times 16\pi r^2$

$\text{and weight of the block W}=\text{density}\times \text{volume}\times g=\frac{\rho }{3}\times (h\times 16\pi r^2)\times g$

$\Rightarrow \rho g(h_1+h)\times 12\pi r^2-\rho g{h}_1\times 16\pi r^2=\frac{\rho }{3}\times (h\times 16\pi r^2)\times g\Rightarrow (h_1+h)12-16h_1=\frac{16}{3}h\Rightarrow h_1=\frac{5h}{3}$