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

A wooden piece floats half submerged in a tub of water. If the system is transferred to a lift ascending with acceleration the wooden piece will

A cork is submerged in water by a spring attached to the bottom of a bowl. When the bowl is kept in an elevator moving with acceleration downwards, the length of spring

The reading of spring balance when a block is suspended from it in air, is $60\,N$. This reading is changed to $40\, N$ when the block is immersed in water. The specific density of the block is

A solid cube and a solid sphere both made of same material are completely submerged in water but to different depths. The sphere and the cube have same surface area. The buoyant force is

  • [KVPY 2012]

Two solids $A$  and $ B$  float in water. It is observed that $A$  floats with $\frac{1}{2}$ of its body immersed in water and $ B$  floats with $\frac{1}{4}$ of its volume above the water level. The ratio of the density of $ A$  to that of $B$  is