Given below are two statements :

Statement I : The average momentum of a molecule in a sample of an ideal gas depends on temperature.

Statement II : The rms speed of oxygen molecules in a gas is $$v$$. If the temperature is doubled and the oxygen molecules dissociate into oxygen atoms, the rms speed will become $$2 v$$.

In the light of the above statements, choose the correct answer from the options given below :

In the wave equation

$$ y=0.5 \sin \frac{2 \pi}{\lambda}(400 \mathrm{t}-x) \,\mathrm{m} $$

the velocity of the wave will be:

Two capacitors, each having capacitance $$40 \,\mu \mathrm{F}$$ are connected in series. The space between one of the capacitors is filled with dielectric material of dielectric constant $$\mathrm{K}$$ such that the equivalence capacitance of the system became $$24 \,\mu \mathrm{F}$$. The value of $$\mathrm{K}$$ will be :

A wire of resistance R₁ is drawn out so that its length is increased by twice of its original length. The ratio of new resistance to original resistance is :