A transverse wave given by $$y=2 \sin (0.01 x+30 t)$$ moves on a stretched string from one end to another end in 0.5 second. If '$$x$$' and '$$y$$' are in $$\mathrm{cm}$$ and '$$\mathrm{t}$$' is in second, then the length of the string is

The translational kinetic energy of the molecules of a gas at absolute temperature (T) can be doubled

When a light of wavelength '$$\lambda$$' falls on the emitter of a photocells, maximum speed of emitted photoelectrons is '$$\mathrm{V}$$'. If the incident wavelength is changed to $$\frac{2 \lambda}{3}$$, maximum speed of emitted photoelectrons will be

A polyatomic gas $$(\gamma=4 / 3)$$ is compressed to $$\left(\frac{1}{8}\right)^{\text {th }}$$ of its volume adiabatically. If its initial pressure is $$\mathrm{P}_0$$, its new pressure will be