Two identical wires of rubber and iron are stretched by the same weight. The number of atoms in the iron wire will be:

Two identical steel cubes (masses $50\,g$,side $1\,cm$) collide head-on face to face with a speed of $10\,cm/s$ each. Find the maximum compression of each. Young's modulus for steel $Y = 2 \times 10^{11}\,N/m^2$.

$A$ sphere of mass $4 \,kg$ is attached to one end of a steel wire of length $1 \,m$ and radius $1 \,mm$. It is whirled in a vertical circle with an angular velocity $10 \,rad \,s^{-1}$. If the sphere is at the lowest point of its path,the elongation in the wire is . . . . . . $(g=10 \,ms^{-2}, Y_{\text{steel}}=20 \times 10^{10} \,Nm^{-2})$ (in $\,mm$)

Two blocks of masses $1 \,kg$ and $2 \,kg$ are connected by a metal wire going over a smooth pulley. The breaking stress of metal is $\frac{40}{3 \pi} \times 10^6 \,N m^{-2}$. What should be the minimum radius of the wire used if it should not break (in $mm$)? $(g = 10 \,m s^{-2})$

Why is the maximum height of a mountain about $\sim 10 \ km$ on Earth?

Each of three blocks $P$,$Q$ and $R$ shown in the figure has a mass of $3 \,kg$. Each of the wires $A$ and $B$ has a cross-sectional area of $0.005 \,cm^2$ and a Young's modulus of $2 \times 10^{11} \,N \,m^{-2}$. Neglecting friction,the longitudinal strain on wire $B$ is . . . . . . $\times 10^{-4}$. (Take $g=10 \,m/s^2$)