The mutual inductances between the primary coil and the secondary coils of linear variable differential transformer (LVDT) shown in the figure are $M_1$ and $M_2$. Assume that the self-inductances $L_{s1}$ and $L_{s2}$ remain constant and are independent of $x$. When x=0, $M_1=M_2=M_0.$ When $x$ is in the range $\underline+ 10 mm,$ $M_1$ and $M_2$ change linearly with x. At $\text{x=+10 mm or -10 mm,}$ the change in the magnitude of $M_1$ and $M_2$ is $0.25\: M_0$. For a particular displacement x=D, the voltage across the detector becoms zero when $|V_2|=1.25|V_1|$. The value of $D$ (in mm, rounded off to one decimal place) is _______
