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 solid part of the specimen has a density of 5 multiplied by 10cubedkg/meter cubed.What fraction of the specimen's apparent volume is solid

Answer 1

Lets make it simple: Let the size of the rock in air have a mass of 200kg, in water, half that.

So the bouyancy from water is 100kg*g, meaning the rock volume is 100kg/densitywater= 100kg/(1000kg/m^3)=.1m^3

now, the rock consist of two parts: hollow, and rock.

volume rockpart=massrock/density=100kg/(5E3kg/m^3= 20E-3 m^3

fraction which is solid= .020/.1=20 percent. Check my work

fraction which is solid=

Answer 2

A mass m = 4.3 kg is attached to a vertical spring with k = 210 N/m and is set into motion. What is the frequency of the oscillation?

Answer 3

Volume of solid in sample is 40%

Density of sample = 2 (from informaton)

If,for example, sample is 100cm3:
Volume(solid)=40 cm3 (from above)
Since density of rock is 5, therefore mass of rock (from 40 cm3)=200g
Therefore density of sample=200/100=2
This verifies the above density for the sample (according to info provided)