1. Use the formula for rms speed

For a gas at temperature $T$,

$v_{\text{rms}} = \sqrt{\frac{3RT}{M}}$

where $M$ is the molar mass.

At the same temperature, rms speed varies inversely as the square root of molar mass:

$v_{\text{rms}} \propto \frac{1}{\sqrt{M}}$

2. Relate oxygen and hydrogen speeds

Given:

• Oxygen gas: $v_O = 160\ \text{m/s}$
• Need hydrogen speed: $v_H$

Using proportionality,

$\frac{v_H}{v_O} = \sqrt{\frac{M_O}{M_H}}$

3. Substitute molar masses

For gases:

• $M_{O_2} = 32$
• $M_{H_2} = 2$

So,

$\frac{v_H}{160} = \sqrt{\frac{32}{2}} = \sqrt{16} = 4$

Thus,

$v_H = 160 \times 4 = 640\ \text{m/s}$

4. Match with options

$\boxed{640\ \text{m/s}}$

So the correct option is A.