Question

A uniform disk of mass $M$ and radius $R$ is mounted on a fixed horizontal axis. A block of mass $m$ hangs from a massless string that is wrapped around the rim of the disk. The magnitude of the acceleration of the falling block ($m$) is:

• A. $\frac{2M}{M+2m}g$
• B. $\frac{2m}{M+2m}g$
• C. $\frac{4M}{M+2m}g$
• D. $\frac{9M}{M+3m}g$

Answer 1

The correct option is B $\frac{2m}{M+2m}g$

$R\times T=I\alpha I=\frac{M{R}^2}{2}\Rightarrow R\times T=\frac{M{R}^2}{2}\times \alpha \alpha =\frac{2T}{MR}\Rightarrow mg-T=maT=mg-ma\Rightarrow \frac{a}{R}=\frac{2(mg-ma)}{MR}Ma=2mg-2maa=\frac{2mg}{M+2m}$