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 `4.9xx10^(-7) m^(2)`. If the mass is pulled a little in the vertically downward direction and released , it performs `SHM` with angular frequency `140 rad s^(-1)`. If the young's modulus of the material of the wire is ` pxx10^(9) Nm^(-2)`, find the value of `p`.

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`