A uniform rod of length $L$ has a mass per unit length $\lambda$ and area of cross-section $A$. If the Young's modulus of the rod is $Y$. Then elongation in the rod due to its own weight is ………..

A wire elongates by $l$ $mm$ when a load $W$ is hanged from it. If the wire goes over a pulley and two weights $W$ each are hung at the two ends, the elongation of the wire will be (in $mm$)

A truck is pulling a car out of a ditch by means of a steel cable that is $9.1\,m$ long and has a radius of $5\,mm$, when the car just begins to move the tension in the cable is $800\,N$. How much has the cable stretched ? (Young’s modulus for steel is $ 2 \times 10^{11}\,Nm^{-2}$)

On applying a stress of $20 \times {10^8}N/{m^2}$ the length of a perfectly elastic wire is doubled. Its Young’s modulus will be

The extension of a wire by the application of load is $3$ $mm.$ The extension in a wire of the same material and length but half the radius by the same load is….. $mm$