A steel ring of radius r and cross-section area A is fitted on to a wooden disc of radius R (R > r). If Young's modulus be E, then the force with which the steel ring is expanded is

Initial length (circumference) of the ring =2πrFinal length (circumference) of the ring =2πrChange in length =2πR−2πr Strain = Change in length  Original length =2π(R−r)2πr=R−rr Now Young's modulus, E=F/Al/L=F/A(R−r)/r∴F=AER−rr