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Question

For a gas sample with N0 number of molecules, function N(V) is given by N(V)=dNdV=(3N0V30)V2 for 0<V<Vo and N(V)=0 for V>V0 where dN is the number of molecules in the speed range V to V+dV. The rms speed of the molecules is

A
25V0
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B
35V0
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C
2V0
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D
3V0
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Solution

The correct option is B 35V0
GIven dNdV=(3N0V30)V2

V2rms= dNv2dN

but dN=(3N0V30)v2dV

So
V2rms=(3N0V30)v2dvv2(3N0V30)v2dv (limits |V00)

=V00v4dvV00v2dv=[v55]v00[v33]v00=3v505v30=35v20

Vrms=35V20=35V0

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