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

Here,`m=0.1kg, L=1m,`
`A=4.9xx10^(-7)m^(2),omega=140rad//s`
Let `l` be the extension in wire when mass is suspended from one end of wire. Then`y=(mg)/(A)xx(L)/(l)` …(i)
When mass attached at the end of wire executes SHM, its angular frequency , `omega=sqrt((g)/(l))` or `l=(g)/(omega^(2))`
From (i), `Y=(mg)/(A)xx(L)/((g//omega^(2)))=(mLomega^(2))/(A)`
`=(0.1xx1xx(140)^(2))/(4.9xx10^(-7))=4xx10^(9)N//m^(2)`
`:. nxx10^(9)=4xx10^(9)` ltbr. or `n=4`