$A$ steel wire of length $L$ and area of cross-section $A$ is suspended from a rigid support. If $Y$ is the Young's modulus of the material of the wire and $\alpha$ is the coefficient of linear expansion,then the increase in tension when the temperature falls by $t^{\circ} C$ is:

When a wire of length $L$ clamped at one end is pulled by a force $F$ from the other end,its length increases by $l$. If the radius of the wire and the applied force were halved,then the increase in its length is

Two identical wires of substances $P$ and $Q$ are subjected to equal stretching force along the length. If the elongation of $Q$ is more than that of $P$,then

Four identical hollow cylindrical columns of mild steel support a big structure of mass $50,000 \; kg$. The inner and outer radii of each column are $30 \; cm$ and $60 \; cm$ respectively. Assuming the load distribution to be uniform,calculate the compressional strain of each column. (Take Young's modulus of mild steel $Y = 2.0 \times 10^{11} \; Pa$ and $g = 9.8 \; m/s^2$)

$A$ steel rod has a radius of $10 \,mm$ and a length of $1 \,m$. $A$ $80 \,kN$ force stretches it along its length. If the Young's modulus of the rod is $2 \times 10^{11} \,N/m^2$, then the change in length is

Two wires of same length having radius of $2 \ mm$ and $1.5 \ mm$ respectively are loaded with same weights. Extension of the second wire is double than that of the first wire. What is the ratio of the Young's modulus of the first wire to that of the second wire?