$A$ copper wire of length $4.0 \, m$ and area of cross-section $1.2 \, cm^2$ is stretched with a force of $4.8 \times 10^3 \, N$. If Young's modulus for copper is $1.2 \times 10^{11} \, N/m^2$,the increase in the length of the wire will be:

Two wires made of the same material are clamped rigidly at one end and pulled by the same force on the other end. The length and the radius of the first wire are three times those of the second wire. If $x$ is the increase in the length of the first wire,then the increase in the length of the second wire is

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..... $mm$.

Two masses $m_1$ and $m_2$ are connected by a light string passing over a pulley as shown in the figure. If the cross-sectional area of the string is $S$,its length is $L$,and its Young's modulus is $Y$,what is the elongation in the string?

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:

$A$ bar is subjected to axial forces as shown. If $E$ is the modulus of elasticity of the bar and $A$ is its cross-section area,its total elongation will be: