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

Two concentric circular coils having radii ' $r_1{ }^{\prime}$ and ' $r_2$ ' $\left(r_2 \ll r_1\right)$ are placed co-axially with centres coinciding. The mutual inductance of the arrangement is ( $\mu_0=$ permeability of free space) (Both coils have single turn)

An ordinary body cools from ' $4 \theta^{\prime}$ ' to ' $3 \theta^{\prime}$ ' in ' t ' minutes. The temperature of that body after next 't' minutes is (Assume Newton's law of cooling and room temperature is $\theta$)