Hint: \(P=\frac{1}{3}\frac{mN}{V}v^{2}_{rms}\)
Step: Find the resultant pressure of the gas.
The pressure of the gas is given by;
\(P=\frac{1}{3}\frac{mN}{V}v^{2}_{rms}\)
When the mass of the gas molecules is halved and their rms speed is doubled then the resultant pressure of the gas is;
\(P’=\frac{1}{3}\frac{\left(\frac{m}{2}\right)N}{V}(2v)^{2}_{rms}= \frac{4}{2}\times \frac{1}{3}\frac{mN}{V}v^{2}_{rms}\)
\(\Rightarrow P’ = 2P\)
Hence, option (1) is the correct answer.
