$A$ $0.1 \,kg$ mass is suspended from a wire of negligible mass. The length of the wire is $1 \,m$ and its cross-sectional area is $4.9 \times 10^{-7} \,m^2$. If the mass is pulled a little in the vertically downward direction and released, it performs simple harmonic motion of angular frequency $140 \,rad \,s^{-1}$. If the Young's modulus of the material of the wire is $n \times 10^9 \,N \,m^{-2}$, the value of $n$ is

Young's modulus of a perfectly rigid body material is

The following four wires are made of the same material. If the same tension is applied to each,the wire having the largest extension is

$A$ steel wire of length $L$ at $40^{\circ}C$ is suspended from the ceiling and then a mass $m$ is hung from its free end. The wire is cooled down from $40^{\circ}C$ to $30^{\circ}C$ to regain its original length $L$. The coefficient of linear thermal expansion of the steel is $10^{-5} /^{\circ}C$,Young's modulus of steel is $10^{11} N/m^2$,and the radius of the wire is $1 mm$. Assume that $L \gg$ diameter of the wire. Then the value of $m$ in $kg$ is nearly:

When a load $W$ is hung from a wire of length $2L$,it just breaks. Now this wire is completely melted and a new wire of length $L$ is formed. If the load $W$ is hung from this new wire,what happens?

Two blocks of mass $2 \ kg$ and $4 \ kg$ are connected by a metal wire going over a smooth pulley as shown in the figure. The radius of the wire is $4.0 \times 10^{-5} \ m$ and Young's modulus of the metal is $2.0 \times 10^{11} \ N/m^2$. The longitudinal strain developed in the wire is $\frac{1}{\alpha \pi}$. The value of $\alpha$ is [Use $g = 10 \ m/s^2$].