Find how hollow a rock is given its density and its weight in water

[season89]

Homework Statement

A geologist thinks a rock is hollow. The rock weighed in air is twice as much as when it's in water. Find the fraction of the rock's volume that is solid given the solid part of the rock is 2500kg/m^3 and water is 1000kg/m^3

Homework Equations

rho = mass/volume
Fb = rho*volume*gravity
F(normal) = Force gravity (rock in air) - rho(fwater)*V(displaced)*gravity

The Attempt at a Solution

 

[JaredJames]

Can you please show your attempt at the solution as per PF guidelines.

Jared

 

[season89]

Given that density of solid part of rock is 2500kg/m^3, water is 1000kg/m^3, air has neglibile density and the whole object weighs twice is much in air than in water:

Apparent weight = m(object in air)*g - m(fluid displaced)*g
1/2*m(object in air)*g = m(object in air)*g - m(fluid displaced)g
1/2* rho (object)*V*g = rho (object)*V*g - rho (fluid)*V*g
1/2* rho (object) = rho (object) - rho (fluid)
-1/2*rho (object) = - 1000kg/m^3
rho (object) = 2000kg/m^3

therefore
2000kg/m^3 = x*(solid part) + (1-x)*(air)
2000kg/m^3 = 2500kg/m^3*x
x = 2000/2500 = 0.8 or 80%

 

[rl.bhat]

Your answer is correct.