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 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 uniform wire of radius $r$ is stretched by a $2kg$ weight, the increase in its length is $2.00\, mm$. If the radius of the wire is $r/2$ and other conditions remain the same, the increase in its length is .......... $mm$

Young's moduli of the material of wires $A$ and $B$ are in the ratio of $1: 4$, while its area of cross sections are in the ratio of $1: 3$. If the same amount of load is applied to both the wires, the amount of elongation produced in the wires $A$ and $B$ will be in the ratio of

[Assume length of wires $A$ and $B$ are same]

A steel wire can sustain $100\,kg$ weight without breaking. If the wire is cut into two equal parts, each part can sustain a weight of ......... $kg$

The value of Young's modulus for a perfectly rigid body is ...........

According to Hook’s law of elasticity, if stress is increased, the ratio of stress to strain