The temperature of a metal strip having coefficient of linear expansion $\alpha$ is increased from $T_1$ to $T_2$ resulting in increase of its length by $\Delta L_1$. The temperature is further increased from $T_2$ to $T_3$ such that the increase in its length is $\Delta L_2$.

Given $T_3+T_1=2 T_2$ and $T_2-T_1=\Delta T$, the value of $\Delta L_2$ is $\_\_\_\_$ .

A uniform disc of radius $R$ and mass $M$ is free to oscillate about the axis $A$ as shown in the figure. For small oscillations the time period is $\_\_\_\_$ .

(g is acceleration due to gravity)

A rigid dipole undergoes a simple harmonic motion about its centre in the presence of an electric field $\overrightarrow{\mathrm{E}}_1=\mathrm{E}_0 \hat{x}$. If another electric field $\overrightarrow{\mathrm{E}}_2=2 \mathrm{E}_0(\hat{y}+\hat{z})$ is introduced to the system, what will be the percentage change in the frequency of the oscillation (approximate)?

From the circuit given below, the capacitance between terminals $A$ and $B$ shown in the circuit is $\_\_\_\_$ $\mu \mathrm{F}$.

(take $C_1=C_2=C_3=1 \mu \mathrm{~F}$ and $C_4=2 \mu \mathrm{~F}$.)