Question

A cylinder of radius R is filled with water up to a
height H, so that the thrust on wall is equal to that
on the bottom. The height H and R are related as
H=R/2
H=R
H=2R
H=R/3​

Answer 1

Answer:

At hight x pressure is pgx and it is working on 2πRdx area so force

$df = \rho \: gx(2\pi \: r)dx \\ f = 2\pi \rho g \int _{0} ^{h} xdx \\ f = 2\pi \rho g ( \frac{ {h}^{2} }{2} ) = \pi \rho g {h}^{2}$

Now trust on buttom will be equal to mg.

$mg = \rho \: vg = \rho(\pi {r}^{2} h)g$

Given both are equal

$\pi \rho g {h}^{2} = \pi \rho {r}^{2} hg \\ r = h$