A black body has maximum wavelength '$$\lambda_{\mathrm{m}}$$' at temperature $$2000 \mathrm{~K}$$. Its corresponding wavelength at temperature $$3000 \mathrm{~K}$$ will be

A monoatomic gas at pressure '$$\mathrm{P}$$' having volume '$$\mathrm{V}$$' expands isothermally to a volume $$2 \mathrm{~V}$$ and then adiabatically to a volume $$16 \mathrm{~V}$$. The final pressure of the gas is $$\left(\gamma=\frac{5}{3}\right)$$

A particle moves in a circular orbit of radius '$$r$$' under a central attractive force, $$F=-\frac{k}{r}$$, where $$\mathrm{k}$$ is a constant. The periodic time of its motion is proportional to

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