Question

The velocities of three molecules are $3v,4v$ and $12v$ respectively. Their root mean square speed will be

• A. $6.5v$
• B. $8.5v$
• C. $7.5v$
• D. $9.5v$

Answer 1

The correct option is C $7.5v$

Given:
Velocities of three molecules $=3v,4v$ and $12v$
To find:
Root mean square speed, $v_{rms}=?$

We know, by definition, root mean square speed is given by
$v_{rms}=\sqrt{\frac{v_1^2+v_2^2+v_3^2}{3}}$
$\Rightarrow v_{rms}=\sqrt{\frac{(3v{)}^2+(4v{)}^2+(12v{)}^2}{3}}$
$\Rightarrow v_{rms}=7.5v$