Kinetic Theory Of Gases Question 21

Question: Four molecules have speeds 2 km/sec, 3 km/sec, 4 km/sec and 5 km/sec. The root mean square speed of these molecules (in km/sec) is

Options:

A) $ \sqrt{54/4} $

B) $ \sqrt{54/2} $

C) 3.5

D) $ 3\sqrt{3} $

Show Answer

Answer:

Correct Answer: A

Solution:

[a] $ v _{rms}={{[ \frac{{{( 2 )}^{2}}+{{( 3 )}^{2}}+{{( 4 )}^{2}}+{{( 5 )}^{2}}}{4} ]}^{1/2}} $

$ =\sqrt{[ \frac{54}{4} ]} $