A cord is wrapped on a pulley (disk) of mass M and radius R as shown in figure. To one end of the cord, a block of mass M is connected as shown and to other end in (a) a force of 2 M g and in (b) a bl

Question

A cord is wrapped on a pulley (disk) of mass $M$ and radius $R$ as shown in figure. To one end of the cord, a block of mass $M$ is connected as shown and to other end in (a) a force of $2 M g$ and in (b) a block of mass $2 M$ . Let angular acceleration of the disk in $A$ and $B$ is $α_{A}$ and $α_{B}$ respectively, then (cord is not slipping on the pulley)

Source diagram

TestHub · Accepted Answer

For (a), T 2 ​ = 2 M g , T 1 ​ − M g = M a A ​ . ( T 2 ​ − T 1 ​ ) R = 2 1 ​ M R 2 α A ​ a A ​ = R α A ​ gives α A ​ = 3 R 2 g ​ . For (b), T 1 ​ − M g = M a B ​ , 2 M g − T 2 ​ = 2 M a B ​ . The same torque equation gives α B ​ = 7 R 2 g ​ . Hence α A ​ > α B ​ .

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