Question

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

• A. $2.4\, cm ^{3}$
• B. $2.4\, m ^{3}$
• C. $4.2 \,m ^{3}$
• D. $4.2\, mm ^{3}$

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]
$\therefore V=\frac{50}{19.3}=2.6 \,cm ^{3}$
Now, loss in wt. of gold in water $=$ Thrust due to water
$\Rightarrow 50\, g -45\, g =\left[ V + V _{ c }\right] \rho_{w} g$
$\Rightarrow 5=\left(2.6+V_{c}\right) \times 1$
$\Rightarrow V_{ c }=2.4 \,cm ^{3}$