Answer
$300m/s$
Work Step by Step
We know that $v_{rms}$ is given as
$v_{rms}=\sqrt{\frac{3PV}{Nm}}.......eq(1)$
Now, when pressure and volume are both halved then
$v_{rms}^{\prime}=\sqrt{\frac{3\frac{P}{2}\frac{V}{2}}{Nm}}$
This simplifies to:
$v_{rms}^{\prime}=\frac{1}{2}\sqrt{\frac{3PV}{Nm}}$
Frome eq(1), substituting the value of $v_{rms}$
$\implies v_{rms}^{\prime}=\frac{1}{2} v_{rms}$
$\implies v_{rms}^{\prime}=\frac{1}{2} (600)=300m/s$
