Wires $A$ and $B$ are connected with blocks $P$ and $Q$ as shown. The ratio of lengths,radii,and Young's modulus of wires $A$ and $B$ are $r, 2r$,and $3r$ respectively ($r$ is a constant). Find the mass of block $P$ if the ratio of the increase in their corresponding lengths is $1/(6r^2)$. The mass of block $Q$ is $3M$.

$A$ metal rod is fixed rigidly at two ends so as to prevent its thermal expansion. If $L$, $\alpha$, and $Y$ denote the length of the rod, the coefficient of linear thermal expansion, and the Young's modulus of its material respectively, then for an increase in temperature of the rod by $\Delta T$, the longitudinal stress developed in the rod is

$A$ steel rod of length $1\,m$ and area of cross-section $1\,cm^2$ is heated from $0\,^{\circ}C$ to $200\,^{\circ}C$ without being allowed to extend or bend. Find the tension produced in the rod $(Y = 2.0 \times 10^{11}\,N/m^2, \alpha = 10^{-5} \,^{\circ}C^{-1})$.

The correct increasing order for the modulus of elasticity for copper,steel,glass,and rubber is:

What is Young's modulus? Explain it,and provide its unit and dimensional formula.

$A$ steel ring of radius $r$ and cross-sectional area $A$ is fitted onto a wooden disc of radius $R$ $(R > r)$. If Young's modulus is $Y$,then the force with which the steel ring is expanded is