A cylinder with adiabatic walls is closed at both ends and is divided into two compartments by a frictionless adiabatic piston. Ideal gas is filled in both (left and right) the compartments at same $P, V$,

T. Heating is started from left side until pressure changes to $27 \mathrm{P} / 8$. If initial volume of each compartment was 9 litres then the final volume in right-hand side compartment is $\_\_\_\_$ litres. (for this ideal gas $\mathrm{C}_{\mathrm{P}} / \mathrm{C}_{\mathrm{V}}=1.5$ )

For an electromagnetic wave propagating through vacuum, $\vec{k}, \vec{E}$ and $\omega$ represent propagation vector, electric field and angular frequency, respectively. The magnetic field associated with this wave is represented by:

Two identical bodies A and B of equal masses have initial velocities $\overrightarrow{v_1}=4 \hat{i} \mathrm{~m} / \mathrm{s}$ and $\overrightarrow{v_2}=4 \hat{j} \mathrm{~m} / \mathrm{s}$ respectively. The body A has acceleration $\overrightarrow{a_1}=6 \hat{i}+6 \hat{j} \mathrm{~m} / \mathrm{s}^2$ while the acceleration of the other body B is zero. The centre of mass of the two bodies moves in $\_\_\_\_$ path.

Figure represents the extension $(\Delta l)$ of a wire of length 1 meter, suspended from the ceiling of the room at one end with a load $W$ connected to the other end. If the cross-sectional area of the wire is $10^{-5} \mathrm{~m}^2$ then the Young's modulus of the wire is $\_\_\_\_$ $\mathrm{N} / \mathrm{m}^2$.