For a gas sample with `N_(0)` number of molecules, function N (V) is given by : `N (V) = (dN )/(dV) = (( 2 N_(0))/(V _(0) ^(3))) V ^(2)` for `0 lt V lt V _(0) and N (V) = 0` for `V gt V _(0).` Where dN is number of molecules in speed range V to V + DV. The rms speed of the molecules is:

Options

A. `sqrt ((3)/(5)) V _(0)`
B. `sqrt ((2)/(5)) V _(0)`
C. `sqrt 2 V _(0)`
D. `sqrt3 V _(0)`

Answer

A

Explanation

`v _(rms) = [ ( int V ^(2) dN )/( int dN) ] ^( 1//2)= [ (int _(0) ^(v _(0)) V ^(4) dV)/( int _(0) ^( v _(0)) V ^(2) dV ) ] ^( 1//2)=sqrt ((3)/(5)) V _(0)`