An a.c. source of angular frequency '$$\omega$$' is fed across a resistor '$$R$$' and a capacitor '$$C$$' in series. The current registered is I. If now the frequency of source is changed to $$\frac{\omega}{3}$$ (but maintaining the same voltage), the current in the circuit is found to be halved. The ratio of reactance to resistance at the original frequency '$$\omega$$' will be

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