When open pipe is closed from one end third overtone of closed pipe is higher in frequency by $$150 \mathrm{~Hz}$$, then second overtone of open pipe. The fundamental frequency of open end pipe will be

A ray of light is incident at an angle $$i$$ on one face of prism of small angle $$A$$ and emerges normally from the other surface. $$\mu$$ is the refractive index of the material of the prism. The angle of incidence is

Two small drops of mercury each of radius $$r$$ coalesce to form a large single drop. The ratio of the total surface energies before and after the change is

A solid cylinder of radius $$r$$ and mass $$M$$ rolls down an inclined plane of height $$h$$. When it reaches the bottom of the plane, then its rotational kinetic energy is ($$g=$$ acceleration due to gravity)