Question 151: Properties of Matter

Question

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 ${{27} \over 8}$ w.r.t water,
the value of r is :

Accepted Answer

${4 \over 3}\pi \left( {{R^3} - {r^3}} \right){p_m}\,g = {4 \over 3}\pi {R^3}{p_w}\,g$
$1 - {\left( {{r \over R}} \right)^3} = {8 \over {27}}$
$ \Rightarrow {r \over R} = {\left( {{{19} \over {27}}} \right)^{1/3}} = {{{{19}^{1/3}}} \over 3}$
$ = 0.88 \simeq {8 \over 9}$
![](https://imagex.cdn.examgoal.net/1kjtn896b/6a46d57a-3cd7-40b3-aedd-810d94ca1169/82e17c30-54a3-11eb-bc03-4b67b2efa0ee/file-1kjtn896c-303w.png)

Answer

${{2} \over 3}$R

Answer

${{4} \over 9}$R

Answer

${{1} \over 3}$R

Answer

${{8} \over 9}$R

Properties of Matter

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 {{27} \over 8} w.r.t water, the value of r is :

Choose the correct answer: