$\frac{2}{5} \mathrm{M}^{\prime} \mathrm{R}^{\prime 2}$
$\mathrm{M}=\mathrm{M}^{\prime}$ and $\mathrm{V}=\mathrm{V}^{\prime}(\mathrm{Volume})$
$\pi \mathrm{R}^{2} \cdot \frac{\mathrm{R}}{6}=\frac{4 \pi}{3} \mathrm{R}^{3} \rightarrow \mathrm{R}^{\prime}=\frac{\mathrm{R}}{2}$
$I’=\frac{2}{5} M\left(\frac{R}{2}\right)^{2}=\frac{1}{5}\left(\frac{M R^{2}}{2}\right)=\frac{I}{5}$
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Statement $(I)$ : The mean free path of gas molecules is inversely proportional to square of molecular diameter.
Statement $(II)$ : Average kinetic energy of gas molecules is directly proportional to absolute temperature of gas.
In the light of the above statements, choose the correct answer from the option given below:
Statements $I:$ The temperature of a gas is $-73^{\circ}\,C$. When the gas is heated to $527^{\circ}\,C$, the root mean square speed of the molecules is doubled.
Statement $II:$ The product of pressure and volume of an ideal gas will be equal to translational kinetic energy of the molecules.
In the light of the above statements, choose the correct answer from the options given below :
$STATEMENT-2$ By the principle of conservation of energy, the total kinetic energies of both the cylinders are identical when they reach the bottom of the incline.