In the given figure,if the dimensions of the two wires are same but materials are different,then Young's modulus is ........

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

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:

Young's moduli of two wires $A$ and $B$ are in the ratio $7 : 4$. Wire $A$ is $2\, m$ long and has radius $R$. Wire $B$ is $1.5\, m$ long and has radius $2\, mm$. If the two wires stretch by the same length for a given load,then the value of $R$ is close to ......... $mm$.

The lengths of four wires $A, B, C$ and $D$ made of the same material are $1 \,m, 2 \,m, 3 \,m$ and $4 \,m$ respectively. The radii of the wires $A, B, C$ and $D$ are $0.2 \,mm, 0.4 \,mm, 0.6 \,mm$ and $0.8 \,mm$ respectively. For the same applied tension, the elongation is more in which wire?

$A$ thick brass wire of length $L$ and density $\rho$ is suspended from a rigid support. Due to its own weight,$\ell$ is the increase in length. The Young's modulus $Y$ of the brass wire in terms of density is $(g = \text{acceleration due to gravity})$