Two wires are made of the same material and have the same volume. However wire $1$ has crosssectional area $A$ and wire $2$ has cross-section area $3A$. If the length of wire $1$ increases by $\Delta x$ on applying force $F$, how much force is needed to stretch wire $2$ by the same amount?

A steel wire is $1 \,m$ long and $1 \,mm ^2$ in area of cross-section. If it takes $200 \,N$ to stretch this wire by $1 \,mm$, how much force will be required to stretch a wire of the same material as well as diameter from its normal length of $10 \,m$ to a length of $1002 \,cm$ is ........ $N$

A $0.1 \mathrm{~kg}$ mass is suspended from a wire of negligible mass. The length of the wire is $1 \mathrm{~m}$ and its crosssectional area is $4.9 \times 10^{-7} \mathrm{~m}^2$. If the mass is pulled a little in the vertically downward direction and released, it performs simple harmonic motion of angular frequency $140 \ \mathrm{rad} \mathrm{s}^{-1}$. If the Young's modulus of the material of the wire is $\mathrm{n} \times 10^9 \mathrm{Nm}^{-2}$, the value of $\mathrm{n}$ is

Two wires $A$ and $B$ of same length, same area of cross-section having the same Young's modulus are heated to the same range of temperature. If the coefficient of linear expansion of $A$ is $3/2$ times of that of wire $B$. The ratio of the forces produced in two wires will be

Four identical hollow cylindrical columns of mild steel support a big structure of mass $50,000 \;kg$. The inner and outer radii of each column are $30$ and $60\; cm$ respectively. Assuming the load distribution to be uniform, calculate the compressional strain of each column.

The Young's modulus of a wire of length $L$ and radius $r$ is $Y$. If the length is reduced to $\frac{L}{2}$ and radius is $\frac{r}{2}$ , then the Young's modulus will be