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.
A metallic rod having area of cross section $A$, Young’s modulus $Y$, coefficient of linear expansion $\alpha $ and length $L$ tied with two strong pillars. If the rod is heated through a temperature $t\,^oC$ then how much force is produced in rod ?
The Young's modulus of a steel wire of length $6\,m$ and cross-sectional area $3\,mm ^2$, is $2 \times 11^{11}\,N / m ^2$. The wire is suspended from its support on a given planet. A block of mass $4\,kg$ is attached to the free end of the wire. The acceleration due to gravity on the planet is $\frac{1}{4}$ of its value on the earth. The elongation of wire is (Take $g$ on the earth $=10$ $\left.m / s ^2\right):$
In an experiment to determine the Young's modulus, steel wires of five different lengths $(1,2,3,4$ and $5\,m )$ but of same cross section $\left(2\,mm ^{2}\right)$ were taken and curves between extension and load were obtained. The slope (extension/load) of the curves were plotted with the wire length and the following graph is obtained. If the Young's modulus of given steel wires is $x \times 10^{11}\,Nm ^{-2}$, then the value of $x$ is
A rod of length $l$ and area of cross-section $A$ is heated from $0°C$ to $100°C$. The rod is so placed that it is not allowed to increase in length, then the force developed is proportional to