A steel ring of radius r and cross-sectional area A is fitted onto a wooden disc of radius R (R gt r). If the Young's modulus of steel is Y, then the force with which the steel ring is expanded is ..........

A steel ring of radius r and cross-sectional area A is fitted onto a w

1.	A steel ring of radius r and cross-sectional area A is fitted onto a wooden disc of radius R (R gt r). If the Young's modulus of steel is Y, then the force with which the steel ring is expanded is ..........
Answer» `AY (R )/(r )` `AY [ (R-r)/(r )]` `Y/A [ (R-r)/(r )]` `(Yr)/(AR)` Solution :CIRCUMFERENCE of wooden disc `=2pi R` Circumference of steel RING `L = 2pi r ` Increase in circumference of steel ring `l= 2pi R - 2pi r` `= 2pi (R-r)` STRAIN `= l/L = (2pi (R-r))/( 2pi r ) = (R-r)/(r)` Now, Young.s modulus `Y= ("stress")/("strain") = ((F)/(A))/( (R-r)/(r))` `therefore F = AY[ (R-r)/(r)]`