Answer
$\rho=1640~kg/m^3$
Work Step by Step
Find the Buoyant force in water:
$\sum F = T+B-W=0$
$B=W-T=39.2~N-28.4~N=10.8~N$
Find the volume of the rock:
$V={B \over \rho_{water}g}={10.8~N \over (1000~kg/m^3)(9.8~m/s^2)}=1.1 \times 10^{-3}~m^3$
Find the Buoyant force in the unknown liquid:
$\sum F = T+B-W=0$
$B=39.2~N-21.5~N=17.7~N$
Use the volume of the rock and the buoyant force in the liquid to find the density of the liquid:
$\rho = {B \over Vg}={17.7~N \over (1.1 \times 10^{-3}~m^3)(9.8~m/s^2)}=1640~kg/m^3$
