If $C_{1}, C_{2}, C_{3}, . . .$ represent the speeds of $n_{1}, n_{2}, n_{3}$ , .... molecules, then the root mean square speed is:

{[\frac{n_{1} C_{1}^{2} + n_{2} C_{2}^{3} + n_{3} C_{3}^{2} + . . . .}{n_{1} + n_{2} + n + 3 + . . .}]}^{1 / 2}

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{[\frac{n_{1}^{2} C_{1}^{2} + n_{2}^{2} C_{2}^{3} + n_{3}^{2} C_{3}^{2} + . . . .}{n_{1} + n_{2} + n + 3 + . . .}]}^{1 / 2}

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[\frac{(n_{1} C_{1}^{2})^{1 / 2}}{n_{1}} + \frac{(n_{2} C_{2}^{2})^{1 / 2}}{n_{2}} + \frac{(n_{3} C_{3}^{2})^{1 / 2}}{n_{3}} + . . . .]

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{[\frac{(n_{1} C_{1} + n_{2} C_{2} + n_{3} C_{3} + . . . .)^{2}}{(n_{1} + n_{2} + n + 3 + . . .)}]}^{1 / 2}

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Solution

The correct option is B ${[\frac{n_{1} C_{1}^{2} + n_{2} C_{2}^{3} + n_{3} C_{3}^{2} + . . . .}{n_{1} + n_{2} + n + 3 + . . .}]}^{1 / 2}$
As we know,
$u_{r m s} = {[\frac{C_{1}^{2} + C_{2}^{2} + C_{3}^{2} + . . . .}{n_{1} + n_{2} + n_{3} + . . .}]}^{1 / 2}$
so here,
$C_{1}, C_{2}, C_{3}, . . .$ represent the speeds of $n_{1}, n_{2}, n_{3}$ , .... molecules
$u_{r m s} = {[\frac{n_{1} C_{1}^{2} + n_{2} C_{2}^{2} + n_{3} C_{3}^{2} + . . . .}{n_{1} + n_{2} + n_{3} + . . .}]}^{1 / 2}$

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Similar questions

If $C_{1}, C_{2}, C_{3}$ .........represent the speeds of $n_{1}, n_{2}, n_{3}$ ......... molecules, then the root mean square speed is _____.

Q. If

C_{1}, C_{2}, C_{3}

.....represent the speeds of

n_{1}, n_{2}, n_{3}

.....molecules, then the root mean square speed is
(a)

{(\frac{n_{1} C_{1}^{2} + n_{2} C_{2}^{2} + n_{3} C_{1}^{3} + \dots}{n_{1} + n_{2} + n_{3} + \dots})}^{\frac{1}{2}}

(b)

\frac{(n_{1} C_{1}^{2} + n_{2} C_{2}^{2} + n_{3} C_{1}^{3} + \dots)^{\frac{1}{2}}}{n_{1} + n_{2} + n_{3} + \dots}

(c)

\frac{(n_{1} C_{1}^{2})^{\frac{1}{2}}}{n_{1}} + \frac{(n_{2} C_{2}^{2})^{\frac{1}{2}}}{n_{2}} + \frac{(n_{3} C_{1}^{3})^{\frac{1}{2}}}{n_{3}} + \dots

(d)

{[\frac{(n_{1} C_{1}^{2} + n_{2} C_{2}^{2} + n_{3} C_{1}^{3} + \dots]^{2}}{(n_{1} + n_{2} + n_{3} + \dots)}]}^{\frac{1}{2}}

If $C_{1}, C_{2}, C_{3}$ .........represent the speeds of $n_{1}, n_{2}, n_{3}$ ......... molecules, then the root mean square speed is _____.

If $C_{1}$ , $C_{2}$ , $C_{3}$ ........ represent the speeds of $n_{1}$ , $n_{2}$ , $n_{3}$ ........ molecules, then the root mean square speed is.......

Q. If

n_{1}, n_{2}

and

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are the fundamental frequencies of three segments into which a string is divided, then the original fundamental frequency n of the string is given by:
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origin

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If C1,C2,C3,... represent the speeds of n1,n2,n3, .... molecules, then the root mean square speed is:

The correct option is B [n1C21+n2C32+n3C23+....n1+n2+n+3+...]1/2As we know,urms=[C21+C22+C23+....n1+n2+n3+...]1/2so here, C1,C2,C3,... represent the speeds of n1,n2,n3, .... moleculesurms=[n1C21+n2C22+n3C23+....n1+n2+n3+...]1/2

If $C_{1}, C_{2}, C_{3}, . . .$ represent the speeds of $n_{1}, n_{2}, n_{3}$ , .... molecules, then the root mean square speed is: