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 Mg and in (b) a block of mass $2 M$. Let angular acceleration of the disk in $A$ and $B$ is $\alpha_{A}$ and $\alpha_{B}$, respectively, then (cord is not slipping on the pulley).

Question

Aicharya · Accepted Answer

In figure, $(T_{2}-T_{1}) R=\frac{MR^{2}}{2} \alpha_{A}$
$T_{1}-Mg=Ma_{A}$
$\begin{aligned} T_{2}&=2 Mg \\ a_{A}&=Ra_{A} \\ \alpha_{A}&=\frac{2 g}{3 R} \end{aligned}$
From figure,
$(T_{2}-T_{1}) \times R=\frac{M R^{2}}{2} a_{B}$
$T_{1}-Mg=M a_{B}$
$2 Mg-T_{2}=2 Ma_{B}$
$\begin{aligned} a_{B}&=r a_{B} \\ \alpha_{B}&=\frac{2 g}{7 R} \end{aligned}$
So, $\alpha_{A} > \alpha_{B}$

A cord is wrapped on a pulley (disk) of mass \(M\) and radius \(R\) as shown in figure. To one end of the…

Solution