1. Use the formula for r.m.s. speed

For a गैस molecule,

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

where:

• $R$ = gas constant
• $T$ = absolute temperature in K
• $M$ = molar mass

2. Condition for equal r.m.s. speeds

If hydrogen and oxygen have the same r.m.s. speed, then

$\sqrt{\frac{3RT_H}{M_H}} = \sqrt{\frac{3RT_O}{M_O}}$

Squaring both sides:

$\frac{T_H}{M_H} = \frac{T_O}{M_O}$

So,

$T_H = T_O\cdot \frac{M_H}{M_O}$

3. Substitute known values

Oxygen molecule: $O_2$, so

$M_O = 32$

Hydrogen molecule: $H_2$, so

$M_H = 2$

Given oxygen temperature:

$47^\circ C = 47 + 273 = 320\,K$

Therefore,

$T_H = 320 \cdot \frac{2}{32} = 320 \cdot \frac{1}{16} = 20\,K$

4. Match with options

$20\,K$ corresponds to Option A.

5. Check the stored answer

Stored correct answer = A

Our derived answer = A

So they agree.