Internal energy of $$n_1$$ moles of hydrogen at temperature '$$T$$' is equal to internal energy of '$$n_2$$' moles of helium at temperature $$2 T$$, then the ratio $$\mathrm{n}_1: \mathrm{n}_2$$ is

[Degree of freedom of $$\mathrm{He}=3$$, Degree of freedom of $$\mathrm{H}_2=5$$]

A body of mass '$$\mathrm{m}$$' and radius of gyration '$$\mathrm{K}$$' has an angular momentum $$\mathrm{L}$$. Its angular velocity is

Two beams of light having intensities I and 4I interfere to produce a fringe pattern on a screen. The phase difference between the beams is $$\pi / 2$$ at point $$\mathrm{A}$$ and $$\pi$$ at point $$\mathrm{B}$$. Then the difference between the resultant intensities at $$\mathrm{A}$$ and $$\mathrm{B}$$ is

A body is executing S.H.M. under the action of force having maximum magntude $$50 \mathrm{~N}$$. When its energy is half kinetic and half potential; the magnitude of the force acting on the particle is