MHTCET 23 Apr 2025 Shift 2 Paper

Concept:The root mean square (r.m.s.) speed of gas molecules is the square root of the mean of the squares of their individual speeds.Explanation:The r.m.s. speed is calculated using the formula:$$v_{\text{rms}} = \sqrt{\frac{v_1^2 + v_2^2 + \dots + v_n^2}{n}}$$where $v_1, v_2, \dots, v_n$ are the speeds of the individual molecules and $n$ is the total number of molecules.Here, the six given speeds are $2$, $5$, $3$, $6$, $3$, and $5$ m/s, so $n = 6$.Substitute these values into the formula:$$v_{\text{rms}} = \sqrt{\frac{2^2 + 5^2 + 3^2 + 6^2 + 3^2 + 5^2}{6}}$$$$v_{\text{rms}} = \sqrt{\frac{4 + 25 + 9 + 36 + 9 + 25}{6}}$$$$v_{\text{rms}} = \sqrt{\frac{108}{6}} = \sqrt{18}$$$$v_{\text{rms}} = 3\sqrt{2} \approx 4.24 \ \text{m/s}$$Answer:The r.m.s. speed of the gas molecules is approximately $4.24$ m/s, which corresponds to option C.