A circuit element $$\mathrm{X}$$ when connected to an a.c. supply of peak voltage $$100 \mathrm{~V}$$ gives a peak current of $$5 \mathrm{~A}$$ which is in phase with the voltage. A second element $$\mathrm{Y}$$ when connected to the same a.c. supply also gives the same value of peak current which lags behind the voltage by $$\frac{\pi}{2}$$. If $$\mathrm{X}$$ and $$\mathrm{Y}$$ are connected in series to the same supply, what will be the rms value of the current in ampere?

An unpolarised light beam of intensity $$2 I_{0}$$ is passed through a polaroid P and then through another polaroid Q which is oriented in such a way that its passing axis makes an angle of $$30^{\circ}$$ relative to that of P. The intensity of the emergent light is

An $$\alpha$$ particle and a proton are accelerated from rest through the same potential difference. The ratio of linear momenta acquired by above two particles will be:

An object of mass $$1 \mathrm{~kg}$$ is taken to a height from the surface of earth which is equal to three times the radius of earth. The gain in potential energy of the object will be [If, $$\mathrm{g}=10 \mathrm{~ms}^{-2}$$ and radius of earth $$=6400 \mathrm{~km}$$ ]