A force is applied to a steel wire ' $A$ ', rigidly clamped at one end. As a result elongation in the wire is $0.2\,mm$. If same force is applied to another steel wire ' $B$ ' of double the length and a diameter $2.4$ times that of the wire ' $A$ ', the elongation in the wire ' $B$ ' will be $............\times 10^{-2}\,mm$ (wires having uniform circular cross sections)

Longitudinal stress of $1\,kg/m{m^2}$ is applied on a wire. The percentage increase in length is $(Y = {10^{11}}\,N/{m^2})$

A pan with set of weights is attached with a light spring. When disturbed, the mass-spring system oscillates with a time period of $0.6$ $s.$ When some additional weights are added then time period is $0.7s.$ The extension caused by the additional weights is approximately given by ......... $cm$

Two steel wires of same length but radii $r$ and $2r$ are connected together end to end and tied to a wall as shown. The force stretches the combination by $10\ mm$. How far does the midpoint $A$ move ............ $mm$

Four uniform wires of the same material are stretched by the same force. The dimensions of wire are as given below. The one which has the minimum elongation has

A steel wire of length $3.2 m \left( Y _{ S }=2.0 \times 10^{11}\,Nm ^{-2}\right)$ and a copper wire of length $4.4\,M$ $\left( Y _{ C }=1.1 \times 10^{11}\,Nm ^{-2}\right)$, both of radius $1.4\,mm$ are connected end to end. When stretched by a load, the net elongation is found to be $1.4\,mm$. The load applied, in Newton, will be. (Given $\pi=\frac{22}{7}$)