Q. A uniform disk of mass $M$ and radius $R$ is mounted on a fixed horizontal axis. A block of mass $m$ hangs from a mass less 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) $\frac{M + 2m}{2M}g$
D) $\frac{2M + m}{2M}g$
Explanation
(b) Using $a = \frac{g}{1 + \frac{I}{mR^{2}}}$
$a = \frac{g}{1 + \frac{MR^{2}}{2mR^{2}}}\ \ \ \ \ \left\lbrack I = \frac{1}{2}MR^{2} \right\rbrack$
$\Rightarrow a = \frac{2m}{M + 2m}g$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.