If $\delta$ is the depression produced in a beam of length $L$,breadth $b$ and thickness $d$,when a load $W$ is placed at the mid-point,then:

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 $mm$)?

Two wires of different materials have same length $L$ and same diameter $d$. The second wire is connected at the end of the first wire and forms one single wire of double the length. This wire is subjected to a stretching force $F$ to produce an elongation $\ell$. The two wires have:

As shown in the figure,a light uniform rod $PQ$ of length $150 \ cm$ is suspended from the ceiling horizontally using two metal wires $A$ and $B$ tied to the ends of the rod. The ratios of the radii and the Young's moduli of the materials of the two wires $A$ and $B$ are respectively $2:3$ and $3:2$. The position at which a weight should be suspended from the rod such that the elongations of the two wires become equal is

In the determination of Young's modulus $\left(Y=\frac{4 MLg}{\pi \ell d^2}\right)$ by using Searle's method,a wire of length $L=2 \ m$ and diameter $d=0.5 \ mm$ is used. For a load $M=2.5 \ kg$,an extension $\ell=0.25 \ mm$ in the length of the wire is observed. Quantities $d$ and $\ell$ are measured using a screw gauge and a micrometer,respectively. They have the same pitch of $0.5 \ mm$. The number of divisions on their circular scale is $100$. The contributions to the maximum probable error of the $Y$ measurement:

$A$ steel rail of length $5\,m$ and area of cross-section $40\,cm^2$ is prevented from expanding along its length while the temperature rises by $10\,^{\circ}C$. If the coefficient of linear expansion and Young's modulus of steel are $1.2\times10^{-5}\,K^{-1}$ and $2\times10^{11}\,N/m^2$ respectively,the force developed in the rail is approximately: