解:$(1)$由图知,$G=10\ \text {N},$浸没时$F=6\ \text {N}$
$F_{浮}=G-F=10\ \text {N}-6\ \text {N}=4\ \text {N}$
$(2)m=\frac {G}{g}=\frac {10\ \text {N}}{10\ \text {N/kg}}=1\ \text {kg}$
$ρ_1=\frac {m }{V}=\frac {1\ \text {kg}}{ 50×8×10^{-6}\ \text m^3}=2.5×10^{3}\ \text {kg/m}^3 $
$(3)ρ_液=\frac {F_浮}{gV_排}=\frac { 4\ \text {N}}{10\ \text {N/kg}×50×8×10^{-6}\ \text m^3}=1 ×10^{3}\ \text {kg/m}^3$