A black reactangular surface of area '$$a$$' emits energy '$$\mathrm{E}$$' per second at $$27^{\circ} \mathrm{C}$$. If length and breadth is reduced to $$\left(\frac{1}{3}\right)^{\text {rd }}$$ of initial value and temperature is raised to $$327^{\circ} \mathrm{C}$$ then energy emitted per second becomes

A closed organ pipe of length '$$\mathrm{L}_c$$' and an open organ pipe of length '$$\mathrm{L}_{\mathrm{o}}$$' contain different gases of densities '$$\rho_1$$' and '$$\rho_2$$' respectively. The compressibility of the gases is the same in both the pipes. The gases are vibrating in their first overtone with the same frequency. What is the length of open organ pipe?

The moment of inertia of a circular disc of radius $$2 \mathrm{~m}$$ and mass $$1 \mathrm{~kg}$$ about an axis XY passing through its centre of mass and perpendicular to the plane of the disc is $$2 \mathrm{~kg} \mathrm{~m}^2$$. The moment of inertia about an axis parallel to the axis $$\mathrm{XY}$$ and passing through the edge of the disc is

A progressive wave of frequency 50 Hz is travelling with velocity 350 m/s through a medium. The change in phase at a given time interval of 0.01 second is