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.

Question

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.

Infinity Learn · Accepted Answer

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,$$C+a$$→$$C0=$$−α$$r+A$$ 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=$$α$$r+A$$                …$$(ii)From$$ $$(i) and (ii), we $$geta=ArR+A$$ or $$aA=R+rr=1+Rr=1+4=5$$

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