Question

To verify her suspicion that a rock specimen is hollow, a geologist weighs the specimen in air and in water. She finds that the specimen weighs twice as much in air as it does in water. The density of the solid part of the specimen is 4.13 × 103 kg/m3. What fraction of the specimen’s apparent volume is solid?

Answer 1

As we know that;

= Vsolid is the solid part of the specimen,

So, v is the volume of the total solid

In air,

= Weight of the specimen W = m*g

Then,

In water,

The apparent weight of the specimen W' = W - Fb

So, W' = W/2

= Fb = buoyancy fore = dw*V*g

= W' = W - dw*V*g

= W' = W/2

Then,

= W/2 = W - dw*V*g

= W/2 = dw*V*g

= m*g/2 = dw*V*g

= m/2 = dw*v

So,

= Vsolid*dsolid = dw*V*2

put the values in given formula,

= Vsolid = (1000/4130)*2*V

= Vsolid = 0.484 V

fraction = vsolid/v = 0.484 <----answer

% = 42.5 %