A solid sphere $(A)$ of mass $5 m$ and a spherical shell $(B)$ of mass $m$, both having same radius, are placed on a rough surface. When a force of same magnitude is applied tangentially at the highest points of $A$ and $B$, they start rolling without slipping with an acceleration of $a_A$ and $a_B$, respectively. The ratio of $a_A$ and $a_B$ is $\_\_\_\_$ .

A body of mass 1 kg moves along a straight line with a velocity $v=2 x^2$. The work done by the body during displacement from $x=0$ to 5 m is $\_\_\_\_$ J.

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: