Question

A piece of gold weights $50g$ in air and $45g$ in water. If there is a cavity inside the piece of gold, then find its volume [Density of gold $=19.3g/cc]$.

• A. $2.4c{m}^3$
• B. $2.4m^3$
• C. $4.2m^3$
• D. $4.2m{m}^3$

Answer 1

Answer: (A)

Let $V_c$ is the volume of cavity and $V$ is the actual volume of gold piece [excluding volume of cavity]
$\therefore V=\frac{50}{19.3}=2.6c{m}^3$
Now, loss in wt. of gold in water $=$ Thrust due to water
$\Rightarrow 50g-45g=\left[V+V_c\right]{\rho }_{w}g$
$\Rightarrow 5=\left(2.6+V_c\right)\times 1$
$\Rightarrow V_c=2.4c{m}^3$