Saurabh Koranglekar
Last Activity: 4 Years ago
To solve this problem, we need to understand the relationship between the root mean square (r.m.s.) speed of gas molecules and the number of molecules present.
Step 1: Recall the r.m.s. speed formula
The r.m.s. speed of gas molecules is given by the formula:
v_rms = √(3RT/M)
Where:
v_rms = r.m.s. speed
R = universal gas constant
T = temperature (in Kelvin)
M = molar mass of the gas
Notice that the r.m.s. speed depends only on the temperature and the type of gas (molar mass). It is independent of the number of molecules.
Step 2: Effect of gas leakage
Since the problem states that 25% of the gas leaks out, the number of molecules is reduced. However, the r.m.s. speed remains unchanged because temperature remains constant.
Step 3: Conclusion
The r.m.s. speed of the remaining molecules is the same as the initial r.m.s. speed.
Answer: (d) 200 m/s