A copper wire of negligible mass, length l and corss-section A is kept on a smooth horizontal tabel with one end fiexed. A ball of mass m is attached to the other end. The wire and the ball are rotating with an angular velocity `omega`. If elongation in the wire is `Deltal`, obtain the expression for the Young's modulus.

Explanation

When the ball attached at one end of wire is rotating, then the restoring force in the wire is equal to the centripetal force on the ball.
Centripetal force `F=m r omega^(2) = m//omega^(2)`
As `Y=F/A xx l/(Delta l ) or F=(YADeltal)/(l)`
`:. (YADeltal)/(l) = m//omega^(2) or Y=(ml^(2)omega^(2))/(ADeltal)`.