Answer
The density of the sphere is $750~kg/m^3$
Work Step by Step
The sum of the sphere's weight and the tension is equal to the buoyant force on the sphere. The buoyant force is equal to the weight of water that is displaced by the sphere. Let $\rho_w$ be the density of water. We can find the volume of the sphere as:
$F_B = Mg+T$
$\rho_w~V~g = Mg+\frac{Mg}{3}$
$V = \frac{4M}{3\rho_w}$
We then find the density of the sphere as:
$\rho = \frac{M}{V}$
$\rho = \frac{M}{(\frac{4M}{3\rho_w})}$
$\rho = \frac{3\rho_w}{4}$
$\rho = \frac{(3)(1000~kg/m^3)}{4}$
$\rho = 750~kg/m^3$
The density of the sphere is $750~kg/m^3$.
