A horizontal steel railroad track has a length of $100 \,m$, when the temperature is $25^{\circ} C$. The track is constrained from expanding or bending. The stress on the track on a hot summer day, when the temperature is $40^{\circ} C$ is ............. $\times 10^7\,Pa$ (Note : The linear coefficient of thermal expansion for steel is $1.1 \times 10^{-5} /{ }^{\circ} C$ and the Young's modulus of steel is $2 \times 10^{11} \,Pa$ )

A rigid massless rod of length $6\ L$ is suspended horizontally by means of two elasticrods $PQ$ and $RS$ as given figure. Their area of cross section, young's modulus and lengths are mentioned in figure. Find deflection of end $S$ in equilibrium state. Free end of rigid rod is pushed down by a constant force . $A$ is area of cross section, $Y$ is young's modulus of elasticity

When a weight of $10\, kg$ is suspended from a copper wire of length $3$ metres and diameter $0.4\, mm,$ its length increases by $2.4\, cm$. If the diameter of the wire is doubled, then the extension in its length will be ........ $cm$

Two rods of different materials having coefficients of linear expansion ${\alpha _1},\,{\alpha _2}$ and Young's moduli ${Y_1}$ and ${Y_2}$ respectively are fixed between two rigid massive walls. The rods are heated such that they undergo the same increase in temperature. There is no bending of rods. If ${\alpha _1}:{\alpha _2} = 2:3$, the thermal stresses developed in the two rods are equally provided ${Y_1}:{Y_2}$ is equal to

Two steel wires of same length but radii $r$ and $2r$ are connected together end to end and tied to a wall as shown. The force stretches the combination by $10\ mm$. How far does the midpoint $A$ move ............ $mm$

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