For an ideal gas the density of the gas is $$\rho_0$$ when temperature and pressure of the gas are $$T_0$$ and $$P_0$$ respectively. When the temperature of the gas is $$2 \mathrm{~T}_0$$, its pressure will be $$3 \mathrm{P}_0$$. The new density will be

The temperature gradient in a rod of length $$75 \mathrm{~cm}$$ is $$40^{\circ} \mathrm{C} / \mathrm{m}$$. If the temperature of cooler end of the rod is $$10^{\circ} \mathrm{C}$$, then the temperature of hotter end is

In an oscillating LC circuit, the maximum charge on the capacitor is '$$Q$$'. When the energy is stored equally between the electric and magnetic fields, the charge on the capacitor becomes

A body of mass '$$\mathrm{m}$$' is raised through a height above the earth's surface so that the increase in potential energy is $$\frac{\mathrm{mgR}}{5}$$. The height to which the body is raised is ( $$\mathrm{R}=$$ radius of earth, $$\mathrm{g}=$$ acceleration due to gravity)