A disc of mass \( m \) and radius \( R \) placed on a smooth horizontal table as shown in figure...

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A disc of mass \( m \) and radius \( R \) placed on a smooth horizontal table as shown in figure. A light ideal string passes through the disc such that the one end of the string is attached to a small body of mass \( m \) and the other end is being pulled with a force \( F \). The circumference of the disc is sufficiently rough so that the string does not slip over it. Find acceleration of the small body.
(1) \( \frac{F}{4 m} \)
(2) \( \frac{F}{m} \)
(3) \( \frac{F}{2 m} \)
(4) \( \frac{F}{3 m} \)
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