Answer:
The density is [tex]\rho_z = 2544 \ kg /m^3[/tex]
Explanation:
From the question we are told that
The mass of the rock is [tex]m_r = 1.80 \ kg[/tex]
The tension on the string is [tex]T = 10.8 \ N[/tex]
Generally the weight of the rock is
[tex]W = m * g[/tex]
=> [tex]W = 1.80 * 9.8[/tex]
=> [tex]W = 17.64 \ N[/tex]
Now the upward force(buoyant force) acting on the rock is mathematically evaluated as
[tex]F_f = W - T[/tex]
substituting values
[tex]F_f = 17.64 - 10.8[/tex]
[tex]F_f = 6.84 \ N[/tex]
This buoyant force is mathematically represented as
[tex]F_f = \rho * g * V[/tex]
Here [tex]\rho[/tex] is the density of water and it value is [tex]\rho = 1000\ kg/m^3[/tex]
So
[tex]V = \frac{F_f}{ \rho * g }[/tex]
[tex]V = \frac{6.84}{ 1000 * 9.8 }[/tex]
[tex]V = 0.000698 \ m^3[/tex]
Now for this rock to flow the upward force (buoyant force) must be equal to the length
[tex]F_f = W[/tex]
[tex]\rho_z * g * V = W[/tex]
Here z is smallest density of a liquid in which the rock will float
=> [tex]\rho_z = \frac{W}{ g * V}[/tex]
=> [tex]\rho_z = \frac{17.64}{ 0.000698 * 9.8}[/tex]
=> [tex]\rho_z = 2544 \ kg /m^3[/tex]
