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..... $mm$.

The pressure that has to be applied to the ends of a steel wire of length $10 \ cm$ to keep its length constant when its temperature is raised by $100 \ ^\circ C$ is: (For steel,Young's modulus $Y = 2 \times 10^{11} \ N/m^2$ and coefficient of thermal expansion $\alpha = 1.1 \times 10^{-5} \ K^{-1}$)

To break a wire of $1 \, m$ length, a minimum weight of $40 \, kg \, wt$ is required. Then, the wire of the same material with double the radius and $6 \, m$ length will require a breaking weight of ....... $kg \, wt$.

If the ratio of diameters,lengths,and Young's modulus of steel and copper wires shown in the figure are $p, q$ and $s$ respectively,then the corresponding ratio of increase in their lengths would be

In an experiment,brass and steel wires of length $1\,m$ each with areas of cross-section $1\,mm^2$ are used. The wires are connected in series and one end of the combined wire is connected to a rigid support,while the other end is subjected to an elongation. The stress required to produce a total elongation of $0.2\,mm$ is: [Given: Young's Modulus for steel and brass are $120 \times 10^9\,N/m^2$ and $60 \times 10^9\,N/m^2$ respectively]

The pressure to be applied to the ends of a steel cylinder to keep its length constant upon raising its temperature by $100^{\circ} C$ is (thermal expansion coefficient,$\alpha = 11 \times 10^{-6} / K$,Young's modulus $Y = 200 \text{ GPa}$)