Kinetic Theory question for NEET (NEET 2023), with solution

Answer: (B) $3295°$ C

$v_{rms} = \sqrt{\dfrac{3RT}{M}}$, so $v_{rms} \propto \sqrt{T}$.

"Increased by 3 times" means the speed increases by three times its value, so the new speed is $v + 3v = 4v$. Then
$$T_2 = 16T_1 = 16 \times (273 - 50) = 16 \times 223 = 3568\ \text{K} = 3295°\text{C}$$

(If the new speed were only $3v$, the temperature would be $9 \times 223 = 2007$ K, which is not among the options.)

Solution by Sreeraj P, M.Sc Physics