Two blocks of masses $m$ and $M$ are connected by means of a metal wire of cross-sectional area $A$ passing over a frictionless fixed pulley as shown in the figure. The system is then released. If $M = 2\, m$, then the stress produced in the wire is

Read the following two statements below carefully and state, with reasons, if it is true or false.

$(a)$ The Young’s modulus of rubber is greater than that of steel;

$(b)$ The stretching of a coil is determined by its shear modulus.

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 $\left.g=10\, ms ^{-2}\right)$

The length of metallic wire is $l$. The tension in the wire is $T_1$ for length $l_1$ and tension in the wire is $T_2$ for length $l_2$. Find the original length.

A steel wire of length ' $L$ ' at $40^{\circ}\,C$ is suspended from the ceiling and then a mass ' $m$ ' is hung from its free end. The wire is cooled down from $40^{\circ}\,C$ to $30^{\circ}\,C$ to regain its original length ' $L$ '. The coefficient of linear thermal expansion of the steel is $10^{-5} { }^{\circ}\,C$, Young's modulus of steel is $10^{11}\, N /$ $m ^2$ and radius of the wire is $1\, mm$. Assume that $L \gg $ diameter of the wire. Then the value of ' $m$ ' in $kg$ is nearly

The Young’s modulus for steel is much more than that for rubber. For the same longitudinal strain, which one will have greater tensile stress ?