Two identical disc having radius R are rotating in opposite sense are joined with light rod having frictionless groove A and B and placed on rough horizontal surface as shown in figure. Initially translation velocity of each disc is zero. Then :-

Step-by-step solution

Initially at any instant 't' Finally pure rolling takes place; v_C= ^ R Angular momentum conservation gives (2 ₀ ) mR ^2 2 - mR ^2 2 ( ₀ )=2 mv _ C R + 2 mR ^2 2 ^ aligned & m R^2 2 ₀=2 mv _ C R + mRv _ C ( Since _ . v _ C = ^ R ) . & v _ C = R ₀ 6 aligned Second figure shows that rod is under stress & hence its length will increase. Finally when the discs roll purely, there is no friction & hence no tensile stress Since friction is kinetic therefore mechanical energy will decrease.