Question

Root mean square speed of a gas is $5m{s}^{-1}$. If some molecules out of 10 molecules in all are moving with $7m{s}^{-1}$ and rest all the molecules are moving with $3m{s}^{-1}$, then number of molecules moving with higher speed is .....

Answer 1

As we know,
$u_{rms}=\sqrt{N_1{u}_1^2+N_2{u}_2^2/(N_1+N_2)}$
according to given
$4=\sqrt{x{7}^2+(10-x)3^2/10}$
$x=4$
so number of molecules moving with higher speed is 4.