The area of a cross-section of steel wire is $0.1\,\,cm^2$ and Young's modulus of steel is $2\,\times \,10^{11}\,\,N\,\,m^{-2}.$  The force required to stretch by $0.1\%$ of its length is ......... $N$.

One end of a metal wire is fixed to a ceiling and a load of $2 \mathrm{~kg}$ hangs from the other end. A similar wire is attached to the bottom of the load and another load of $1 \mathrm{~kg}$ hangs from this lower wire. Then the ratio of longitudinal strain of upper wire to that of the lower wire will be____________.

[Area of cross section of wire $=0.005 \mathrm{~cm}^2$, $\mathrm{Y}=2 \times 10^{11}\  \mathrm{Nm}^{-2}$ and $\left.\mathrm{g}=10 \mathrm{~ms}^{-2}\right]$

In a human pyramid in a circus, the entire weight of the balanced group is supported by the legs of a performer who is lying on his back. The combined mass of all the persons performing the act, and the tables, plaques etc. Involved is $280\; kg$. The mass of the performer lying on his back at the bottom of the pyramid is $60\; kg$. Each thighbone (femur) of this performer has a length of $50\; cm$ and an effective radius of $2.0\; cm$. Determine the amount by which each thighbone gets compressed under the extra load.

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 ($Y = 2.0 × 10^{11} Nm^{-2}$)

If in case $A$, elongation in wire of length $L$ is $l$, then for same wire elongation in case $B$ will be ......

The length of an elastic string is a metre when the longitudinal tension is $4\, N$ and $b$ metre when the longitudinal tension is $5\, N$. The length of the string in metre when the longitudinal tension is $9\, N$ is