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Question

A container is filled with a sample of gas having n molecules with speed α,2α,3α,......nα. The ratio of average speed to root mean square speed is :

A
3(n+1)2(2n+1)
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B
(n+1)2(2n+1)
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C
5(2n+2)7(3n+1)
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D
3(n+2)5(3n+2)
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Solution

The correct option is A 3(n+1)2(2n+1)
Average speed is given as,
Vavg=a+2a+3a+...../n
Vavg=a(1+2+3....)/n

Vavg=ann(n+1)2

Vavg=a(n+1)2

Root mean square speed is given as,
Vrms=a2+4a2+9a2+.....n

Vrms=a(n+1)(2n+1)6

VavgVrms=a(n+1)2a(n+1)(2n+1)6

VavgVrms=6(n+1)24(n+1)(2n+1)

VavgVrms=32(n+1)(2n+1).

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