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

The Young's modulus of a wire of length $L$ and radius $r$ is $Y \ N/m^2$. If the length and radius are reduced to $L/2$ and $r/2,$ then its Young's modulus will be

$A$ metal bar of length $L$ and area of cross-section $A$ is clamped between two rigid supports. For the material of the rod,its Young's modulus is $Y$ and coefficient of linear expansion is $\alpha$. If the temperature of the rod is increased by $\Delta t ^\circ C$,the force exerted by the rod on the supports is

$A$ metallic ring of radius $r$ and cross-sectional area $A$ is fitted into a wooden circular disc of radius $R$ $(R > r)$. If the Young's modulus of the material of the ring is $Y$,the force with which the metal ring expands is

$A$ copper wire of length $2.2 \; m$ and a steel wire of length $1.6 \; m$,both of diameter $3.0 \; mm$,are connected end to end. When stretched by a load,the net elongation is found to be $0.70 \; mm$. Obtain the load applied in $N$.

$A$ rigid bar of mass $15\; kg$ is supported symmetrically by three wires each $2.0\; m$ long. Those at each end are of copper and the middle one is of iron. Determine the ratio of their diameters if each is to have the same tension.