A thin uniform circular disc of mass '$$\mathrm{M}$$' and radius '$$R$$' is rotating with angular velocity '$$\omega$$', in a horizontal plane about an axis passing through its centre and perpendicular to its plane. Another disc of same radius but of mass $$\left(\frac{M}{2}\right)$$ is placed gently on the first disc co-axially. The new angular velocity will be

A gas at normal temperature is suddenly compressed to one-fourth of its original volume. If $$\frac{\mathrm{C}_{\mathrm{p}}}{\mathrm{C}_{\mathrm{v}}}=\gamma=1.5$$, then the increase in its temperature is

When light of wavelength $$\lambda$$ is incident on a photosensitive surface the stopping potential is '$$\mathrm{V}$$'. When light of wavelength $$3 \lambda$$ is incident on same surface the stopping potential is $$\frac{\mathrm{V}}{6}$$. Then the threshold wavelength for the surface is

One of the necessary condition for total internal reflection to take place is

( $$\mathrm{i}=$$ angle of incidence, $$\mathrm{i}_{\mathrm{c}}=$$ critical angle)