A string of area of cross-section $4 {\mathrm{mm}}^2$ and length $0.5$ is connected with a rigid body of mass $2 \mathrm{kg}$. The body is rotated in a vertical circular path of radius $0.5 \mathrm{m}$. The body acquires a speed of $5 \mathrm{m} {\mathrm{s}}^{-1}$ at the bottom of the circular path. Strain produced in the string when the body is at the bottom of the circle is _____ $\times {10}^{-5}$. (Use Young's modulus ${10}^{11} \mathrm{N} {\mathrm{m}}^{-2}$ and $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

Given below are two statements: One is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A): Clothes containing oil or grease stains cannot be cleaned by water wash.

Reason (R): Because the angle of contact between the oil/grease and water is obtuse. In light of the above statements, choose the correct answer from the option given below.

The velocity of a small ball of mass $0.3 \mathrm{g}$ and density $8 \mathrm{g} {\mathrm{cc}}^{-1}$ when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is $1.3 \mathrm{g} {\mathrm{cc}}^{-1}$, then the value of viscous force acting on the ball will be $x\times {10}^{-4} \mathrm{N}$, the value of $x$ is _____ .

[use $g=10 \mathrm{m} {\mathrm{s}}^{-2}$]

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 _______.