设 $x\in R$,向量 $\stackrel{\rightharpoonup }{a}=\left(x,1\right),\stackrel{\rightharpoonup }{b}=\left(1,-2\right)$且 $\stackrel{\rightharpoonup }{a}\perp \stackrel{\rightharpoonup }{b}$,则 $\left|\stackrel{\rightharpoonup }{a}\perp \stackrel{\rightharpoonup }{b}\right|$=（）

A．

A. $\sqrt{5}$

B．

B. $\sqrt{10}$

C．

C. $2\sqrt{5}$

D．

D. $10$