A sphere of solid material of relative density $9$ has a concentric spherical cavity and  floats having just sinked in water. If the radius of the sphere be $R$, then the radius of  the  cavity $(r)$ will be related to $R$ as :-

  • A

    $r^3 = \frac{8}{9} R^3$

  • B

    $r^3 = \frac{2}{3} R^3$

  • C

    $r^3 = \frac{\sqrt 8}{3} R^3$

  • D

    $r^3 = \sqrt { \frac{2}{3}} R^3$

Similar Questions

If $W$ be the weight of a body of density $\rho $ in vacuum then its apparent weight in air of density $\sigma $ is

A hemispherical bowl just floats without sinking in a liquid of density $1.2 × 10^3kg/m^3$. If outer diameter and the density of the bowl are $1 m$  and $2 × 10^4 kg/m^3$ respectively, then the inner diameter of the bowl will be........ $m$

A hollow spherical shell at outer radius $R$ floats just submerged under the water surface. The inner radius of the shell is $r$. If the specific gravity of the shell material is $\frac{27}{8}$ $w.r.t.$ water, the value of $r$ is$......R$

  • [JEE MAIN 2020]

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 ......... $cm$

A man is sitting in a boat which is floating in a pond. If the man drinks same water from the pond, the level of water in pond will