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

6.5 v

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8.5 v

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7.5 v

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9.5 v

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Solution

The correct option is C $7.5 v$
Given:
Velocities of three molecules $= 3 v, 4 v$ and $12 v$
To find:
Root mean square speed, $v_{r m s} = ?$

We know, by definition, root mean square speed is given by
$v_{r m s} = \sqrt{\frac{v_{1}^{2} + v_{2}^{2} + v_{3}^{2}}{3}}$
$\Rightarrow v_{r m s} = \sqrt{\frac{(3 v)^{2} + (4 v)^{2} + (12 v)^{2}}{3}}$
$\Rightarrow v_{r m s} = 7.5 v$

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Root Mean Square Speed

Standard XI Physics

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

The correct option is C 7.5 vGiven: Velocities of three molecules =3v, 4v and 12v To find: Root mean square speed, vrms=? We know, by definition, root mean square speed is given by vrms=√v21+v22+v233 ⇒vrms=√(3v)2+(4v)2+(12v)23 ⇒vrms=7.5v

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