Answer :
Answer:
Fraction of the specimen's is 0.4.
Explanation:
We know,
Mass = volume × density
Weigh= mass × g
= volume × density× g
= density× g × volume
[tex]=\rho.g.V[/tex]
An object weighs less submerged due to buoyant force acting on it.
[tex]\therefore W_{wet}= W_{dry}-B[/tex]
[tex]B= W_{dry}-W_{wet}[/tex]
[tex]=W_{\textrm{fluid displaced}}[/tex]
[tex]=\rho_{fluid}. g.V_{submerged}[/tex]
Given that, the weighs of the specimen in dry is twice of the weighs in air.
[tex]W_{wet}=\frac 12W_{dry}[/tex]
Then ,
[tex]B= W_{dry}-W_{wet}[/tex]
[tex]= W_{dry}-\frac12W_{dry}[/tex]
[tex]=\frac12W_{dry}[/tex]
[tex]=\rho_{Rock}. g.V_{Rock}[/tex]
Therefore,
[tex]\rho_{fluid}. g.V_{submerged}=\frac12\rho_{Rock}. g.V_{Rock}[/tex]
[tex]\Rightarrow \rho_{Rock}. g.V_{Rock}=2\rho_{fluid}. g.V_{submerged}[/tex]
[tex]\Rightarrow \frac{.V_{Rock}}{V_{submerged}}=\frac{2\rho_{fluid}. g}{\rho_{Rock}.g}[/tex]
[tex]\Rightarrow \frac{.V_{Rock}}{V_{submerged}}=\frac{2\rho_{fluid}}{\rho_{Rock}}[/tex]
[tex]\Rightarrow \frac{.V_{Rock}}{V_{submerged}}=\frac{2\times 1.0 \times 10^3\ kg /m^3}{5.0\times 10^3 \ kg/m^3}[/tex]
=0.4
Fraction of the specimen's is 0.4.