In the $CGS$ system,the Young's modulus of a steel wire is $2 \times 10^{12} \text{ dyn/cm}^2$. To double the length of a wire of unit cross-sectional area,the force required is:

$A$ wooden wheel of radius $R$ is made of two semicircular parts (see figure). The two parts are held together by a ring made of a metal strip of cross-sectional area $S$ and length $L$. $L$ is slightly less than $2\pi R$. To fit the ring on the wheel,it is heated so that its temperature rises by $\Delta T$ and it just slips over the wheel. As it cools down to the surrounding temperature,it presses the semicircular parts together. If the coefficient of linear expansion of the metal is $\alpha$,and its Young's modulus is $Y$,the force that one part of the wheel applies on the other part is:

Two wires $A$ and $B$ made of the same material and areas of cross-section in the ratio $1: 2$ are stretched by the same force. If the masses of the wires $A$ and $B$ are in the ratio $2: 3$, then the ratio of the elongations of the wires $A$ and $B$ is

When a force of $4 \, N$ is applied to a wire,its length is $a \, m$. When a force of $5 \, N$ is applied,its length is $b \, m$. What will be its length when a force of $9 \, N$ is applied?

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. (Take Young's modulus for bone $Y = 9.4 \times 10^9 \; N/m^2$)

The ratio of the areas of cross-sections of three wires is $1:2:3$ and the ratio of the Young's moduli of their materials is $3:2:1$. If the three wires are of the same length and the same stretching force is applied to the three wires, then the ratio of the elongations of the three wires is