Question

A sphere of radius $R$ and relative density $4$ is hanging with the help of a string such that it remains just inside water. The ratio force exerted by the liquid on upper and lower half of the sphere is (take $P_{atm}=0$)

• A. $1:5$
• B. $1:4$
• C. $2:5$
• D. $1:3$

Answer 1

The correct option is D $1:3$

Total surface area$=4\pi R^2$
Surface area of upper half$=2\pi R^2$
Surface area of lower half$=2\pi R^2$
Average pressure of on upper half$=\left(\frac{h_1+h_2}{2}\right)\rho g=\frac{R}{2}\rho g$
Average pressure of on lower half$=\left(\frac{h_1+h_2}{2}\right)\rho g=\frac{3R}{2}\rho g$
Force upper half$=\frac{R}{2}\rho g\times 2\pi R^2$
Force lower half$=\frac{3R}{2}\rho g\times 2\pi R^2$
Ratio$=\frac{1}{3}$