JEE Physics 2023 Question with Solution

Given: The question asks how root mean square velocity depends on temperature.

Find: The correct proportionality of $v_{\text{rms}}$ with $T$.

The solution states that the root mean square velocity is given by

where $R$ is the universal gas constant, $T$ is temperature in Kelvin, and $M$ is molar mass.

From this formula,

Therefore, the root mean square velocity is proportional to the square root of temperature.

The solution concludes with "The Correct Option is B", but the worked relation $v_{\text{rms}} \propto \sqrt{T}$ matches option C in the listed options. Hence there is a discrepancy between the option label shown in the solution and the actual statement proved by the working. The defensible correct choice from the given options is C.

The answer key says (3) and the solution working gives $v_{\text{rms}} \propto \sqrt{T}$, both of which correspond to option C. However, the solution says "The Correct Option is B". Since the working is the primary source and clearly supports $\sqrt{T}$, the conceptually correct answer is option C.