When a resistance of $100 \Omega$ is connected in series with a galvanometer of resistance G , its range is V . To double its range a resistance of $1000 \Omega$ is connected in series. The value of G is

The angular separation of the central maximum in the Fraunhofer diffraction pattern is measured. The slit is illuminated by the light of wavelength $6000 \mathop A\limits^o$. If the slit is illuminated by light of another wavelength, the angular separation decreases by $20 \%$. The wavelength of light used is

A particle starting from rest moves along the circumference of a circle of radius ' $r$ ' with angular acceleration ' $\alpha$ '. The magnitude of the average velocity in time it completes the small angular displacement ' $\theta$ ' is

If heat energy $\Delta \mathrm{Q}$ is supplied to an ideal diatomic gas, the increase in internal energy is $\Delta U$ and the amount of work done by the gas is $\Delta \mathrm{W}$. The ratio $\Delta \mathrm{W}: \Delta \mathrm{U}: \Delta \mathrm{Q}$ is