A $14.5\; kg$ mass, fastened to the end of a steel wire of unstretched length $1.0 \;m ,$ is whirled in a vertical circle with an angular velocity of $2\;rev/s$ at the bottom of the circle. The cross-sectional area of the wire is $0.065 \;cm ^{2} .$ Calculate the elongation of the wire when the mass is at the lowest point of its path.

A steel uniform rod of length $2L$ cross sectional area $A$ and mass $M$ is set rotating in a horizontal plane about an axis passing through the centre. If $Y$ is the Young’s modulus for steel, find the extension in the length of the rod.

check the statment are True or False $:$

$(a)$ Young’s modulus of rigid body is …..

$(b)$ A wire increases by $10^{-6}$​ times its original length when a stress of
$10^8\,Nm^{-2}$ is applied to it, calculate its Young’s modulus.

$(c)$ The value of Poisson’s ratio for steel is ……

An iron rod of length $2m$ and cross section area of $50\,m{m^2}$, stretched by $0.5\, mm$, when a mass of $250\, kg$ is hung from its lower end. Young's modulus of the iron rod is

In the given figure, two elastic rods $A$ & $B$ are rigidly joined to end supports. $A$ small mass $‘m’$ is moving with velocity $v$ between the rods. All collisions are assumed to be elastic & the surface is given to be frictionless. The time period of small mass $‘m’$ will be : [$A=$ area of cross section, $Y =$ Young’s modulus, $L=$ length of each rod ; here, an elastic rod may be treated as a spring of spring constant $\frac{{YA}}{L}$ ]