A metal string $A$ is suspended from a rigid support and its free end is attached to a block of mass $M$. Second block having mass 2 M is suspended at the bottom of the first block using a string $B$. The area of cross sections of strings $A$ and $B$ are same. The ratio of lengths of strings of $A$ to B is 2 and the ratio of their Young's moduli $\left(Y_A / Y_B\right)$ is 0.5 . The ratio of elongations in $A$ to $B$ is $\_\_\_\_$ .

A water spray gun is attached to a hose of cross sectional area $30 \mathrm{~cm}^2$. The gun comprises of 10 perforations each of cross sectional area of $15 \mathrm{~mm}^2$. If the water flows in the hose with the speed of $50 \mathrm{~cm} / \mathrm{s}$, calculate the speed at which the water flows out from each perforation. (Neglect any edge effects)

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R

Assertion A : If the average kinetic energy of $\mathrm{H}_2$ and $\mathrm{O}_2$ molecules, kept in two different sized containers are same, then their temperatures will be same.

Reason R : The r.m.s speed of $\mathrm{H}_2$ and $\mathrm{O}_2$ molecules are same at same temperature.

Choose the correct answer from the options given below

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 $\_\_\_\_$ .