Consider the situation shown in figure. The force $F$ is equal to the $m_2g/2.$ If the area of cross-section of the string is $A$ and its Young's modulus $Y$, find the strain developed in it. The string is light and there is no friction anywhere
$\frac{{{m_2}g\,\left( {2{m_1} + {m_2}} \right)}}{{AY\,\left( {{m_1} + {m_2}} \right)\,}}$
$\frac{{{m_2}g\,\left( {{m_1} + {m_2}} \right)}}{{2AY\,\left( {{m_1} + {m_2}} \right)\,}}$
$\frac{{{m_2}g\,\left( {2{m_1} + {m_2}} \right)}}{{2AY\,\left( {{m_1} + {m_2}} \right)\,}}$
None of these
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 ........ $cm$
A rod of uniform cross-sectional area $A$ and length $L$ has a weight $W$. It is suspended vertically from a fixed support. If Young's modulus for rod is $Y$, then elongation produced in rod is ......
A steel rod has a radius of $20\,mm$ and a length of $2.0\,m$. A force of $62.8\,kN$ stretches it along its length. Young's modulus of steel is $2.0 \times 10^{11}\,N / m ^2$. The longitudinal strain produced in the wire is $..........\times 10^{-5}$
A steel rod of length $1\,m$ and area of cross section $1\,cm^2$ is heated from $0\,^oC$ to $200\,^oC$ without being allowed to extend or bend. Find the tension produced in the rod $(Y = 2.0 \times 10^{11}\,Nm^{-2}$, $\alpha = 10^{-5} C^{-1})$
Give the relation between shear modulus and Young’s modulus.