Question

A uniform disc of radius R and mass M is free to rotate only about its axis. A string is wrapped over its rim and a body of mass m is tied to the free end of the string as shown in the figure. The body is released from rest. Then the acceleration of the body is :

• A. $\frac{2 mg}{ 2 m + M }$
• B. $\frac{2 Mg}{ 2 m + M }$
• C. $\frac{2 mg}{ 2 M + m }$
• D. $\frac{2 Mg}{ 2 M + m }$

Answer 1

Answer: (B)

$\frac{2 Mg}{ 2 m + M }$

Answer 2

$mg - T = ma$ $RT = I\propto$ $RT = \frac{MR^{2}}{2}. \frac{a}{R}$ $T = \frac{Ma}{2}$ $mg - \frac{Ma}{2} = ma$ $mg - a\left(\frac{M}{2}+m\right)$ $mg - a\left(\frac{M+2m}{2}\right)$ $a = \frac{2mg}{M+2m}$