1. Use the formula for rms speed

For an ideal gas, $v_{\text{rms}} = \sqrt{\frac{3RT}{M}}$ So for a given gas, since $R$ and $M$ are constant, $v_{\text{rms}} \propto \sqrt{T}$

This means rms speed depends only on absolute temperature, not on pressure.

2. Convert temperatures to Kelvin

Initial temperature: $T_1 = 127^\circ C = 127 + 273 = 400\,K$

Final temperature: $T_2 = 227^\circ C = 227 + 273 = 500\,K$

3. Relate the two rms speeds

Given: $v_1 = 200\,\text{m/s}$

Using $\frac{v_2}{v_1} = \sqrt{\frac{T_2}{T_1}}$ we get $v_2 = 200\sqrt{\frac{500}{400}}$

$v_2 = 200\sqrt{\frac{5}{4}}$

$v_2 = 200 \cdot \frac{\sqrt{5}}{2}$

$v_2 = 100\sqrt{5}\,\text{m/s}$

4. Match with options

$100\sqrt{5}\,\text{m/s}$ corresponds to Option B.

5. Comparison with stored answer

Stored correct answer: B

Our derived answer: B

So they agree.