A solid sphere of specific gravity $27$ has a concentric spherical cavity and it just sinks in water. The ratio of cavity radius to that of outer radius of sphere is
$\frac{{{{\left( {28} \right)}^{1/3}}}}{3}$
$\frac{{{{\left( {30} \right)}^{1/3}}}}{3}$
$\frac{{{{\left( {26} \right)}^{1/3}}}}{3}$
$\frac{{{{\left( {24} \right)}^{1/3}}}}{3}$
Asphere of radius $R$ and made of material of relative density $\sigma$ has a concentric cavity of radius $r$. It just floats when placed in a tank full of water. The value of the ratio $R/r$ will be
A wooden cube just floats inside water with a $200 \,gm$ mass placed on it. When the mass is removed, the cube floats with its top surface $2 \,cm$ above the water level. the side of the cube is ......... $cm$
Two cyllinders of same cross-section and length $L$ but made of two material of densities $d_1$ and $d_2$ are cemented together to form a cylinder of length $2L$. The combination floats in a liquid of density $d$ with $a$ length $L/2$ above the surface of the liquid. If $d_1 > d_2$ then:
The vessel shown in the figure has two sections. The lower part is a rectangular vessel with area of cross-section $A$ and height $h$. The upper part is a conical vessel of height $h$ with base area $‘A’$ and top area $‘a’$ and the walls of the vessel are inclined at an angle $30^o$ with the vertical.A liquid of density $\rho$ fills both the sections upto a height $2h$. Neglecting atmospheric pressure.
A solid sphere of radius $r$ is floating at the interface of two immiscible liquids of densities $\rho_1$ and $\rho_2\,\, (\rho_2 > \rho_1),$ half of its volume lying in each. The height of the upper liquid column from the interface of the two liquids is $h.$ The force exerted on the sphere by the upper liquid is $($ atmospheric pressure $= p_0\,\,\&$ acceleration due to gravity is $g) $