A steel ring of radius $r$ and cross-section area $‘A’$ is fitted on to a wooden disc of radius $R(R > r)$. If Young's modulus be $E,$ then the force with which the steel ring is expanded is
$AE\frac{R}{r}$
$AE\left( {\frac{{R - r}}{r}} \right)$
$\frac{E}{A}\left( {\frac{{R - r}}{A}} \right)$
$\frac{{Er}}{{AR}}$
Two wires of the same material have lengths in the ratio 1 : 2 and their radii are in the ratio $1:\sqrt 2 $. If they are stretched by applying equal forces, the increase in their lengths will be in the ratio
A structural steel rod has a radius of $10\,mm$ and length of $1.0\,m.$ A $100\,kN$ force stretches it along its length . Young's modulus of structural steel is $2 \times 10^{11}\,Nm^{-2}.$ The percentage strain is about ....... $\%$
Two identical solid balls, one of ivory and the other of wet-clay are dropped from the same height on the floor. Which one will rise to a greater height after striking the floor and why ?
A uniform heavy rod of mass $20\,kg$. Cross sectional area $0.4\,m ^{2}$ and length $20\,m$ is hanging from a fixed support. Neglecting the lateral contraction, the elongation in the rod due to its own weight is $x \times 10^{-9} m$. The value of $x$ is
(Given. Young's modulus $Y =2 \times 10^{11} Nm ^{-2}$ અને $\left.g=10\, ms ^{-2}\right)$
There are two wire of same material and same length while the diameter of second wire is two times the diameter of first wire, then the ratio of extension produced in the wires by applying same load will be