Answer
The circumference according to the proton frame is $5.1~m$
Work Step by Step
Let $L_0 = 6.3~km$
We can find the circumference $L$ according to the proton frame:
$L = L_0~\sqrt{1-\frac{v^2}{c^2}}$
$L = (6.3~km)~\sqrt{1-\frac{(3.0\times 10^8~m/s - 100~m/s)^2}{(3.0\times 10^8~m/s)^2}}$
$L = (6.3~km)~\sqrt{1-\frac{(299999900~m/s)^2}{(3.0\times 10^8~m/s)^2}}$
$L =0.0051~km = 5.1~m$
The circumference according to the proton frame is $5.1~m$.
