Young's modulus of rubber is $10^4 \ N/m^2$ and the area of cross-section is $2 \ cm^2$. If a force of $2 \times 10^5 \ dynes$ is applied along its length,then its initial length $L$ becomes:

There are two wires of the same material and same length. The diameter of the second wire is two times the diameter of the first wire. What is the ratio of the extensions produced in the wires by applying the same load?

$A$ force $F$ is applied on a wire of radius $r$ and length $L$,and the change in the length of the wire is $l$. If the same force $F$ is applied on a wire of the same material with radius $2r$ and length $2L$,then what is the change in the length of the second wire?

$A$ wire is suspended from a rigid support and a weight $W$ is attached to its free end,causing an extension of $1.0 \, mm$. If the same wire is passed over a pulley and a weight $W$ is attached to each of its two ends,what will be the extension in the wire in $mm$?

$A$ cable is cut to half of its original length. What will be the effect on the increase in its length under a given load?

$A$ wooden wheel of radius $R$ is made of two semicircular parts (see figure). The two parts are held together by a ring made of a metal strip of cross-sectional area $S$ and length $L$. $L$ is slightly less than $2\pi R$. To fit the ring on the wheel,it is heated so that its temperature rises by $\Delta T$ and it just slips over the wheel. As it cools down to the surrounding temperature,it presses the semicircular parts together. If the coefficient of linear expansion of the metal is $\alpha$,and its Young's modulus is $Y$,the force that one part of the wheel applies on the other part is: