Question

A sample of metal weighs $210g$ in air, $140g$ in water and $120g$ in an unknown liquid. Then

• A. the density of the metal is $3g/c{m}^3$
• B. the density of the metal is $7g/c{m}^3$
• C. density of the metal is $4$ times the density of unknown liquid
• D. the metal still float in water

Answer 1

Answer: (A)

the density of the metal is $3g/c{m}^3$

Sample of metal weighs $210g$ in air, we have

$V{\rho }_{m}g=0.21g\Rightarrow V{\rho }_m=0.21....\left(I\right)$

it weighs 140g in water, we have

$0.14g=0.21g-V{\rho }_{w}g\Rightarrow 0.14=0.21-V{\rho }_w\Rightarrow V{\rho }_w=0.07....\left(II\right)$

Dividing $\left(I\right)$ by $\left(II\right)$, we have

$\frac{{\rho }_m}{{\rho }_w}=\frac{0.21}{0.07}=3\Rightarrow {\rho }_m=3{\rho }_w=3\times 1=3gm/c{m}^3$