Question

A piece of copper having an internal cavity weighs $261g$ in air and $221g$ in water. If density of copper is $9gc{c}^{-1}$ then the volume of cavity is

• A. $5cc$
• B. $10cc$
• C. $11cc$
• D. $22cc$

Answer 1

Answer: (C)

$11cc$

Let the total volume be $V$ and volume of cavity be $v$,

So net material volume is $V-v$ , $\rho =9c{c}^{-1}$

Let the density be $\rho =\frac{mass}{netvolume}=\frac{261}{V-v}$

$9=\frac{261}{V-v}$

$V-v=29cc$ ....(1)

Now the buoyancy force on cylinder is $F=261g-221g=40g$

So $F=40g={\rho }_{water}Vg$

$40g=1\times Vg$

$V=40cc$

From equation 1,

$v=40-29=11cc$