The speed of a transverse wave passing through a string of length $50 \mathrm{cm}$ and mass $10 \mathrm{g}$ is $60 \mathrm{m} {\mathrm{s}}^{-1}$. The area of cross-section of the wire is $2.0 {\mathrm{mm}}^2$ and its Young's modulus is $1.2\times {10}^{11} \mathrm{N} {\mathrm{m}}^{-2}$. The extension of the wire over its natural length due to its tension will be $\mathrm{x}\times {10}^{-5} \mathrm{m}$. The value of $x$ is _____ .

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

Assertion (A) : Steel is used in the construction of buildings and bridges.
Reason (R) : Steel is more elastic and its elastic limit is high. 

In the light of above statements, choose the most appropriate answer from the options given below

A spherical ball of radius $1 \mathrm{mm}$ and density $10.5 \mathrm{g} {\mathrm{cc}}^{-1}$ is dropped in glycerine of coefficient of viscosity $9.8$ poise and density $1.5 \mathrm{g} {\mathrm{cc}}^{-1}$. Viscous force on the ball when it attains constant velocity is $3696\times {10}^{-x} \mathrm{N}$. The value of $x$ is

(Given, $g=9.8 \mathrm{m} {\mathrm{s}}^{-2} \text{and} \mathrm{\pi }=\frac{22}{7}$)

As shown in the figure, in an experiment to determine Young's modulus of a wire, the extension-load curve is plotted. The curve is a straight line passing through the origin and makes an angle of $45°$ with the load axis. The length of wire is $62.8 \mathrm{cm}$ and its diameter is $4 \mathrm{mm}$. The Young's modulus is found to be  $\mathrm{x}\times {10}^4 \mathrm{N} {\mathrm{m}}^{-2}$

The value of $x$ is _______.

A fully loaded boeing aircraft has a mass of $5.4\times {10}^5 \mathrm{kg}$. Its total wing area is $500 {\mathrm{m}}^2$. It is in level flight with a speed of $1080 \mathrm{km} {\mathrm{h}}^{-1}$. If the density of air $\rho$ is $1.2 \mathrm{kg} {\mathrm{m}}^{–3}$, the fractional increase in the speed of the air on the upper surface of the wing relative to the lower surface in percentage will be

($g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

A metal block of base area $0.20 {\mathrm{m}}^2$ is placed on a table, as shown in figure. A liquid film of thickness $0.25 \mathrm{mm}$ is inserted between the block and the table. The block is pushed by a horizontal force of $0.1 \mathrm{N}$ and moves with a constant speed. If the viscosity of the liquid is $5.0\times {10}^{–3} \mathrm{Pl}$, the speed of block is ______ $\times {10}^{-3} \mathrm{m} {\mathrm{s}}^{-1}$.