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` Calculate the value of n.

Explanation

Young modules of the material of the wire,
`Y=(F/A)/((DeltaA)/L)=(FL)/(A DeltaL) or,F=((YA)/L)DeltaL`......(1)
IF mass m is pulled by a length `DeltaL` then restoring force developed in the wire,
`F=k DeltaL`…….(2)
Comparing equation (1) and (2) we get ,
`k=(YA)/L`
Angular frequency , `omega=sqrt(K/m)=sqrt((YA)/(mL))`
or,`140=sqrt((ntimes10^9times4.9times10^-7)/(0.1times1))=70sqrtn`
`therefore sqrtn=2 or n=4`