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 :

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

A uniform disc of radius R and mass M is free to r

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Concepts Used:

Newtons Laws of Motion

Newton’s First Law of Motion:

Newton’s 1^st law states that a body at rest or uniform motion will continue to be at rest or uniform motion until and unless a net external force acts on it.

Newton’s Second Law of Motion:

Newton’s 2^nd law states that the acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the object’s mass.

Mathematically, we express the second law of motion as follows:

Newton’s Third Law of Motion:

Newton’s 3^rd law states that there is an equal and opposite reaction for every action.