An electron moves through a uniform magnetic field $\overrightarrow{B}=B_0\hat{\mathrm{i}}+2B_0\hat{\mathrm{j}} \mathrm{T}$. At a particular instant of time, the velocity of electron is $\overrightarrow{u}=3\hat{\mathrm{i}}+5\hat{\mathrm{j}} \mathrm{m} {\mathrm{s}}^{-1}$. If the magnetic force acting on electron is $\overrightarrow{F}=5e\hat{\mathrm{k}} \mathrm{N}$, where $e$ is the charge of electron, then the value of $B_0$ is ____ $\mathrm{T}$.