#### Answer

If the tension is doubled, the speed is 283 m/s

#### Work Step by Step

We can write an expression for the initial speed which is 200 m/s:
$v_1 = \sqrt{\frac{T_1}{\mu}}$
We can find the final speed as:
$v_2 = \sqrt{\frac{T_2}{\mu}}$
$v_2 = \sqrt{\frac{2T_1}{\mu}}$
$v_2 = \sqrt{2}~\sqrt{\frac{T_1}{\mu}}$
$v_2 = \sqrt{2}~v_1$
$v_2 = \sqrt{2}~(200~m/s)$
$v_2 = 283~m/s$
If the tension is doubled, the speed is 283 m/s.