Consider a rod of length $1.0 \ m$ with a cross-sectional area of $0.50 \ cm^2$. The rod supports a $500 \ kg$ platform that hangs attached to the rod's lower end. What is the elongation of the rod under the stress, ignoring the weight of the rod (in $mm$)? Consider Young's modulus to be $10^{11} \ Pa$ and $g = 10 \ m \ s^{-2}$.

With a rise in temperature,the Young's modulus of elasticity

Two wires of different materials have same length $L$ and same diameter $d$. The second wire is connected at the end of the first wire and forms one single wire of double the length. This wire is subjected to a stretching force $F$ to produce an elongation $\ell$. The two wires have:

$A$ wire of length $2\, m$ is made from $10\, cm^3$ of copper. $A$ force $F$ is applied so that its length increases by $2\, mm$. Another wire of length $8\, m$ is made from the same volume of copper. If the same force $F$ is applied to it,its length will increase by ......... $cm$.

$A$ wooden wheel of radius $R$ is made of two semicircular parts. The two parts are held together by a metal ring of cross-sectional area $S$ and length $L$. $L$ is slightly less than $2\pi R$. To fit the ring on the wheel,the ring is heated by a temperature $\Delta T$. 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 exerts on the other is:

Young's modulus of elasticity of a material depends upon