Question

An iron casting containing a number of cavities weights 6000 N in air and 4000 N in water.What is the volume of the cavities in the casting ? Density of iron is $7.87g/c{m}^3$.(Take $g=9.8m/s^2$ and density of water =${10}^{3}kg/m^3$)

• A. $0.2m^3$
• B. $0.9m^3$
• C. $0.13m^3$
• D. $0.12m^3$

Answer 1

Answer: (D)

$0.12m^3$

$\text{vol. of iron}=\frac{\text{mass}}{\text{density}}$

$=\frac{\mathrm{6000}/9.8}{7.87\times {10}^3}=0.078m^3$

Now

diff. in weight $=$ Bougency force

$6000-4000=(0.078+v)\cdot {10}^3\times 10$

$200=(0.078+v){10}^3$

$v+0.078=0.2$

$v=0.12m^3$

Answert-$\left(D\right)$