In Young's double slit experiment, the slits are separated by 0.6 mm and screen is placed at a distance of 1.2 m from slit. It is observed that the tenth bright fringe is at a distance of 8.85 mm from the third dark fringe on the same side. The wavelength of light used is

A charged particle is moving in a uniform magnetic field in a circular path of radius ' $R$ '. When the kinetic energy of the particle is increased to three times, then the new radius will be

In the Bohr model of hydrogen atom, the centripetal force is furnished by the coulomb attraction between the proton and the electron. If ' $r_0$ ' is the radius of the ground state orbit, ' $m$ ' is the mass, ' e ' is the charge on the electron and ' $\varepsilon_0$ ' is the permittivity of vacuum, the speed of the electron is

A Carnot's cycle operating between $T_H=600 \mathrm{~K}$ and $T_c=300 \mathrm{~K}$ produces 1.5 kJ of mechanical work per cycle. The heat transferred to the engine by the reservoir is