When a certain weight is suspended from a long uniform wire,its length increases by $1 \ cm$. If the same weight is suspended from another wire of the same material and length but having a diameter half of the first one,then the increase in length will be ........ $cm$.

Which is more elastic: rubber or steel?

$A$ steel wire of length $L$ at $40^{\circ}C$ is suspended from the ceiling and then a mass $m$ is hung from its free end. The wire is cooled down from $40^{\circ}C$ to $30^{\circ}C$ to regain its original length $L$. The coefficient of linear thermal expansion of the steel is $10^{-5} /^{\circ}C$,Young's modulus of steel is $10^{11} N/m^2$,and the radius of the wire is $1 mm$. Assume that $L \gg$ diameter of the wire. Then the value of $m$ in $kg$ is nearly:

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

$A$ wire of length $L$ and radius $r$ is clamped rigidly at one end. When the other end of the wire is pulled by a force $f$,its length increases by $l$. Another wire of the same material of length $2L$ and radius $2r$ is pulled by a force $2f$. Then the increase in its length 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