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=∫dNv2∫dN
but dN=(3N0V30)v2dV
So V2rms=∫(3N0V30)v2dvv2∫(3N0V30)v2dv (limits |V00)