A compressive force, $F$ is applied at the two ends of a long thin steel rod. It is heated, simultaneously, such that its temperature increases by $\Delta T$. The net change in its length is zero. Let $l$ be the length of the rod, $A$ its area of cross- section, $Y$ its Young's modulus, and $\alpha $ its coefficient of linear expansion. Then, $F$ is equal to

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

There are two wires of same material and same length while the diameter of second wire is $2$ times the diameter of first wire, then ratio of extension produced in the wires by applying same load will be 

The Young's modulus of a steel wire of length $6\,m$ and cross-sectional area $3\,mm ^2$, is $2 \times 11^{11}\,N / m ^2$. The wire is suspended from its support on a given planet. A block of mass $4\,kg$ is attached to the free end of the wire. The acceleration due to gravity on the planet is $\frac{1}{4}$ of its value on the earth. The elongation of wire is  (Take $g$ on the earth $=10$ $\left.m / s ^2\right):$

Two wire $A$ and $B$ are stretched by same force. If, for $A$ and $B, Y_A: Y_B=1: 2, r_A: r_B=3: 1$ and $L_A: L_B=4: 1$, then ratio of their extension $\left(\frac{\Delta L_A}{\Delta L_B}\right)$ will be ………….