Consider a cuboidal vessel `(2Rxx2RxxR)` with as hemispherical cavity of radius `R`, kept at a horizontal smooth surface as shown in the figure. The vessel has very small hole of cross-sectional area "a". Now water of density `rho` is poured into space developed due horizontal surface adn vessel through hole very slowly. When the height of waer level is `h`, the vessel lifts off the surface and liquid leaks through space generated. `(R=2m, rho=10^(3)kg//m^(3),m=9pi kg)`. If the value of `h` is `5kcm`, find the value of `k`.
(Atmospheric pressure `=10^(5)N//m^(2)`).

Answer

6

Explanation

`mg=F_(B)=[piR^(2)h- int_(0)^(h)pi(R^(2)-z^(2))dz]rho gimpliesm=(pih^(3)rho)/3`
`implies h^(3)=(3m)/(pirho)=(3xxpixx9)/(pixx10^(3))impliesh= 3/10=0.3m=30m`