A particle is placed at the point $$A$$ of a frictionless track $$A B C$$ as shown in figure. It is gently pushed towards right. The speed of the particle when it reaches the point B is :

(Take $$g=10 \mathrm{~m} / \mathrm{s}^2$$).

Two thermodynamical processes are shown in the figure. The molar heat capacity for process A and B are $$\mathrm{C}_{\mathrm{A}}$$ and $$\mathrm{C}_{\mathrm{B}}$$. The molar heat capacity at constant pressure and constant volume are represented by $$\mathrm{C_P}$$ and $$\mathrm{C_V}$$, respectively. Choose the correct statement.

The electric field of an electromagnetic wave in free space is represented as $$\overrightarrow{\mathrm{E}}=\mathrm{E}_0 \cos (\omega \mathrm{t}-\mathrm{kz}) \hat{i}$$. The corresponding magnetic induction vector will be :

At which temperature the r.m.s. velocity of a hydrogen molecule equal to that of an oxygen molecule at $$47^{\circ} \mathrm{C}$$ ?