A `0.1kg` mass is suspended from a wire of negligible mass. The length of the wire is 1m and its crosssectional are is `4.9xx10^-7m^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 `nxx10^9 Nm^-2`, the value of n is

Answer

4

Explanation

When a wire of length L, area of cross-section A, Young’s modulus Y is stretched by suspending a mass m, then the mass performs simple harmonic motion with angular frequency
`omega=sqrt((YA)/(mL))`
`140=sqrt((nxx10^(9)xx4.9xx10^(-7))/(0.1xx1))` or
`140xx140=(nxx10^(9)xx4.9xx10^(-7))/(0.1xx1)`
`n=(14xx14xx10^(2))/(49xx10^(2))=4`