In the determination of Young's modulus of elasticity of a wire, a force is applied and extension is recorded. Initial length of wire is $1 \mathrm{m}$. The curve between extension and stress is depicted, then Young's modulus of wire will be:

A rod of length $1000 \mathrm{mm}$ and coefficient of linear expansion $\alpha ={10}^{-4}$ per degree is placed symmetrically between fixed walls separated by $1001 \mathrm{mm}$. Young's modulus of the rod is ${10}^{11}\mathrm{N} {\mathrm{m}}^{-2}$. If the temperature is increased by $20°\mathrm{C},$ then the stress developed in the rod is (in $\mathrm{N} {\mathrm{m}}^2$)

Two forces ${\mathrm{F}}_1$ and ${\mathrm{F}}_2$ act on a thin uniform elastic rod placed in space. Force ${\mathrm{F}}_1$ acts at right end of the rod and ${\mathrm{F}}_2$ acts exactly at centre of rod as shown (both forces act parallel to length of the rod).

(i) ${\mathrm{F}}_1$ causes extension of rod while ${\mathrm{F}}_2$ causes compression.
(ii) ${\mathrm{F}}_1$ and ${\mathrm{F}}_2$ both cause extension of rod.
(iii) ${\mathrm{F}}_1$ causes extension of rod while ${\mathrm{F}}_2$ does not change length of rod. The correct order of True (T) or False (F) statements is

The atmospheric pressure on the earth's surface is $\mathrm{P}$ in $\mathrm{M}.\mathrm{K}.\mathrm{S}$. units. A table of area $2 {\mathrm{m}}^2$ is tilted at $45°$ with the horizontal. The force on the table due to the atmosphere is ($\mathrm{stress} \times \mathrm{area}$).

A body of mass $6.28 \mathrm{kg}$ is suspended from one end of a wire of length $10 \mathrm{m}$ : The radius of the wire is changing uniformly from $19.6\times {10}^{-4} \mathrm{m}$ at one end to $10\times {10}^{-4}\mathrm{m}$ at the other end. Find the change in the length of the wire. $\left[Y=2\times {10}^{11}\mathrm{N} {\mathrm{m}}^{-2}\right]$

Calculate the force $F$ needed to punch a $1.46 \mathrm{cm}$ diameter hole in a steel plate $1.27 \mathrm{cm}$ thick. The ultimate shear strength of steel is $345 \mathrm{MN} {\mathrm{m}}^{-2}$.

A metal wire of length $L_1$ and area of cross section A is attached to a rigid support. Another metal wire of length $L_2$ and of the same cross-sectional area is attached to free end of the first wire. A body of mass $\mathrm{M}$ is then suspended from the free end of the second wire. If $Y_1$ and $Y_2$ are the Young's moduli of the wires respectively, the effective force constant of the system of two wires is

The shear modulus of lead is $2\times {10}^9 \mathrm{Pa}$. A cubic lead slab of side $50 \mathrm{cm}$ is subjected to a shearing force of magnitude $9\times {10}^4 \mathrm{N}$ on its narrow face. The displacement of upper edge is $\Delta l$

What internal pressure in the absence of external pressure can be sustained by a glass spherical flask if in both the cases, wall thickness is equal to $\Delta r=1\mathrm{mm}$ and radius of tube and the flask equals $r=25$ $\mathrm{mm}$? $(\mathrm{S}=493\mathrm{SI}$ $\mathrm{units}$$)$