As shown in the figure, in an experiment to determine Young's modulus of a wire, the extension-load curve is plotted. The curve is a straight line passing through the origin and makes an angle of $45^{\circ}$ with the load axis. The length of wire is $62.8\,cm$ and its diameter is $4\,mm$. The Young's modulus is found to be $x \times$ $10^4\,Nm ^{-2}$. The value of $x$ is

A rubber cord catapult has cross-sectional area $25\,m{m^2}$ and initial length of rubber cord is $10\,cm.$ It is stretched to $5\,cm.$ and then released to project a missile of mass $5gm.$ Taking ${Y_{rubber}} = 5 \times {10^8}N/{m^2}$ velocity of projected missile is ……… $ms^{-1}$

The Young's modulus of a rubber string $8\, cm$ long and density $1.5\,kg/{m^3}$ is $5 \times {10^8}\,N/{m^2}$, is suspended on the ceiling in a room. The increase in length due to its own weight will be

The Young's modulus of steel is twice that of brass. Two wires of same length and of same area of cross section, one of steel and another of brass are suspended from the same roof. If we want the lower ends of the wires to be at the same level, then the weights added to the steel and brass wires must be in the ratio of

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.