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

Answer:

0.00049 m³

3328.54854 kg/m³

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

$v=\dfrac{B}{\rho_w g}\\\Rightarrow v=\dfrac{4.9}{1000\times 9.81}\\\Rightarrow v=0.00049\ m^3$

The volume of the sample is 0.00049 m³

Density is given by

$\rho=\dfrac{m}{v}\\\Rightarrow \rho=\dfrac{W}{gv}\\\Rightarrow \rho=\dfrac{16}{9.81\times 0.00049}\\\Rightarrow \rho=3328.54854\ kg/m^3$

The density is 3328.54854 kg/m³