Question

A hollow sphere of specific gravity $2$, floats when completely immersed in water. If the volume of the sphere is $V$, then the volume of cavity is

• A. $V/2$
• B. $V/8$
• C. $V/4$
• D. $V/3$

Answer 1

The correct option is A $V/2$

When body (sphere) is fully immersed then,

Up thrust = weight of sphere

$\Rightarrow V\times p_{liq}\times g=(V-V_c)p_{sphere}g$

$V=(V-V_c)2$

$V_c=\frac{V}{2}$