Question

The rms speed of a group of $7$ gas molecules having speeds $(6,4,2,0,-2,-4,-6)m/s$ is :

• A. 1.5 m/s
• B. 3.4 m/s
• C. 9 m/s
• D. 4 m/s

Answer 1

Answer: (D)

Square-root of the mean square velocity of gas molecules,
is called root-mean-square velocity (rms).
$v_{rms}=\sqrt{\frac{v_1^2+v_2^2+\dots v_N^2}{N}}$
Given $v_1=6m/s$,
$v_2=4m/s,$
$v_3=2m/s,$
$v_4=0m/s$,
$v_5=-2m/s,$
$v_6=-4m/s,$
$v_7=-6m/s.$
$\therefore U_{\text{rms}}=\sqrt{\frac{(6{)}^2+(4{)}^2+(2{)}^2}{(-2{)}^2+(-4{)}^2+(-6{)}^2}}$
$=\sqrt{\frac{112}{7}}=\sqrt{16}=4m/s$