Question

4 molecules of gas have speeds of 1,2,3,4 cm/s respectively. The root mean square velocity is:

• A. $\sqrt{7.5}$ cm/s
• B. 30 cm/s
• C. 45 cm/s
• D. 15 cm/s

Answer 1

The correct option is A $\sqrt{7.5}$ cm/s

Given that $4$ molecules of gas have speed of $1,2,3$ and $4cm/s$ respectively.

Therefore, the root mean square velocity $\left(v_{r.m.s.}\right)$ will be-

$v_{r.m.s.}=\sqrt{\frac{1^2+2^2+3^2+4^2}{4}}$

$\Rightarrow v_{r.m.s.}=\sqrt{\frac{1+4+9+16}{4}}=\sqrt{7.5}cm/s$

Hence the root mean square velocity is $\sqrt{7.5}cm/s$.