Question

A sphere is just immersed in a liquid. The ratio of hydrostatic force acting on top and bottom half of the sphere is $\frac{F_1}{F_2}=\frac{1}{x}$. The value of x is :

Answer 1

Upthrust on the upper part of the sphere = Volume of displaced liquid $\times \rho L\times g$

$=\frac{1}{3}\pi r^3\rho \times g$

Upthrust on the lower part of the sphere,

$=\frac{1}{2}\times (\frac{2}{3}\pi r^3\rho \times g)+\pi r^3$

$\frac{5}{3}\pi r^3\rho g$

$\frac{F_1}{F_2}=\frac{1}{5}$