Two wires of copper having the lengths in the ratio $4:1$ and their radii in the ratio $1:4$ are stretched by the same force. The ratio of longitudinal strain in the two will be

$A$ metal rod of Young's modulus $Y$ and coefficient of thermal expansion $\alpha$ is held at its two ends such that its length remains invariant. If its temperature is raised by $t^{\circ} C$,the linear stress developed in it is

Evaluate the following statements:
$(a)$ Young's modulus of a rigid body is .....
$(b)$ $A$ wire increases by $10^{-6}$ times its original length when a stress of $10^8 \ N/m^2$ is applied to it. Calculate its Young's modulus.
$(c)$ The value of Poisson's ratio for steel is ......

Copper of fixed volume $V$ is drawn into a wire of length $l$. When this wire is subjected to a constant force $F$,the extension produced in the wire is $\Delta l$. Which of the following graphs is a straight line?

The Young's modulus of a wire of length $L$ and radius $r$ is $Y \, N/m^2$. What will be the Young's modulus of a wire made of the same material with length $L/2$ and radius $r/2$?

One end of the steel rod is clamped to the roof and the other end is attached to a mass of $1000 \,kg$ as shown in the figure. The length of the rod is $50 \,cm$ and its cross-sectional area is $1000 \,mm^2$. The change in the length of the rod due to the weight of the mass is (Young's modulus of steel $= 2 \times 10^{11} \,Nm^{-2}$ and acceleration due to gravity $= 10 \,ms^{-2}$) (in $\,mm$)