check the statment are True or False $:$
$(a)$ Young’s modulus of rigid body is .....
$(b)$ A wire increases by $10^{-6}$ times its original length when a stress of
$10^8\,Nm^{-2}$ is applied to it, calculate its Young’s modulus.
$(c)$ The value of Poisson’s ratio for steel is ......
$(1)$ Infinite.
There is no strain in rigid body.
$\text { hence Young's modulus } =\frac{\text { stress }}{\text { strain }}=\frac{\text { stress }}{0}$
$=\text { infinite }$
$(2)$ $10^{14} \mathrm{Nm}^{2}$
$\mathrm{Y}=\frac{\text { Stress }}{\frac{\Delta l}{l}}=\frac{10^{8}}{10^{-6}}=10^{14} \mathrm{Nm}^{-2}$
$(3)$ $0.28$ to $0.30$
When a certain weight is suspended from a long uniform wire, its length increases by one 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 ........ $cm$
What is the percentage increase in length of a wire of diameter $2.5 \,mm$, stretched by a force of $100 \,kg$ wt is .................. $\%$ ( Young's modulus of elasticity of wire $=12.5 \times 10^{11} \,dyne / cm ^2$ )
A beam of metal supported at the two ends is loaded at the centre. The depression at the centre is proportional to
Four identical hollow cylindrical columns of mild steel support a big structure of mass $50 \times 10^{3} {kg}$, The inner and outer radii of each column are $50\; {cm}$ and $100 \;{cm}$ respectively. Assuming uniform local distribution, calculate the compression strain of each column. [Use $\left.{Y}=2.0 \times 10^{11} \;{Pa}, {g}=9.8\; {m} / {s}^{2}\right]$
With rise in temperature, the Young's modulus of elasticity