Question

An ore sample weighs 16.0 N in air. When the sample is suspended by a light cord and totally immersed in water, the tension in the cord is 11.4 N. Find the total volume and density of the sample?

Answer 1

0.00049 m³

3328.54854 kg/m³

Step-by-step explanation:

W = Weight of ore = 16 N

T = Tension of cord = 11.4 N

B = Buoyant force

g = Acceleration due to gravity = 9.81 m/s²

`\rho_w` = Density of water = 1000 kg/m³

As all the forces are conserved

`T+B-W=0\\\Rightarrow B=W-T\\\Rightarrow B=16-11.4\\\Rightarrow B=4.9\ N`

Volume is given by

`v=(B)/(\rho_w g)\\\Rightarrow v=(4.9)/(1000* 9.81)\\\Rightarrow v=0.00049\ m^3`

The volume of the sample is 0.00049 m³

Density is given by

`\rho=(m)/(v)\\\Rightarrow \rho=(W)/(gv)\\\Rightarrow \rho=(16)/(9.81* 0.00049)\\\Rightarrow \rho=3328.54854\ kg/m^3`

The density is 3328.54854 kg/m³