Overall changes in volume and radii of a uniform cylindrical steel wire are $0.2 \%$ and $0.002 \%$ respectively when subjected to some suitable force. Longitudinal tensile stress acting on the wire is ($Y = 2.0 × 10^{11} Nm^{-2}$)

Two wires of the same material have lengths in the ratio 1 : 2 and their radii are in the ratio $1:\sqrt 2 $. If they are stretched by applying equal forces, the increase in their lengths will be in the ratio

A steel wire of diameter $2 \,mm$ has a breaking strength of $4 \times 10^5 \,N$.the breaking force ……… $\times 10^5 \,N$ of similar steel wire of diameter $1.5 \,mm$ ?

On increasing the length by $0.5\, mm$ in a steel wire of length $2\, m$ and area of cross-section $2\,m{m^2}$, the force required is $[Y$ for steel$ = 2.2 \times {10^{11}}\,N/{m^2}]$

The units of Young ‘s modulus of elasticity are