A bobbin with inner radius r and outer radius R is arranged with light strings and a block as shown in the figure. The strings are not sliding over the cylinder. The system is released from rest. The block and bobbin move down with accelerations a and A respectively. If Rr=4, then find the ration aA.

Let angular acceleration of the bobbin is α as shown.Point B is directly connected with roof through string. It means net acceleration of point B should be zero.a→B=a→B,C+a→C0=−αr+A or α=Ar        …(i)Point A on the bobbin is directly connected with block, it means the acceleration of point A should be same as the acceleration of the block.a→A=a→A,C+a→C0=αr+A                …(ii)From (i) and (ii), we geta=ArR+A or aA=R+rr=1+Rr=1+4=5