$$ \text { Match List I with List II: } $$
| $$ \text { List I } $$ |
$$ \text { List I I} $$ |
||
|---|---|---|---|
| A. | Young's Modulus | I. | $$ \frac{\Delta d}{\Delta L}\left(\frac{L}{d}\right) $$ |
| B. | Compressibility | II. | $$ \frac{F L}{A(\Delta L)} $$ |
| C. | Bulk Modulus | III. | $$ -\frac{1}{\Delta P}\left(\frac{\Delta V}{V}\right) $$ |
| D. | Poisson's Ratio | IV. | $$ -P\left(\frac{V}{\Delta V}\right) $$ |
Choose the correct answer from the options given below:
A submarine is designed to withstand an absolute pressure of 100 atm . How deep can it go below the water surface?
(Consider the density of water $=1000 \mathrm{~kg} \mathrm{~m}^{-3}$, $1 \mathrm{~atm}=1 \times 10^5 \mathrm{~Pa}$ and gravitational acceleration $g=10 \mathrm{~m} / \mathrm{s}^2$ )
Consider a water tank shown in the figure. It has one wall at $x=L$ and can be taken to be very wide in the $z$ direction. When filled with a liquid of surface tension $S$ and density $\rho$, the liquid surface makes angle $\theta_0\left(\theta_0 \ll 1\right)$ with the $x$-axis at $x=L$. If $y(x)$ is the height of the surface then the equation for $y(x)$ is:

(take $\theta(x)=\sin \theta(x)=\tan \theta(x)=\frac{d y}{d x}, g$ is the acceleration due to gravity)
An ideal fluid is flowing in a non-uniform cross-sectional tube $$X Y$$ (as shown in the figure) from end $$X$$ to end $$Y$$. If $$K_1$$ and $$K_2$$ are the kinetic energy per unit volume of the fluid at $$X$$ and $$Y$$ respectively, then the correct option is :

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