A spool of thread of mass \( M \) is placed on an inclined smooth plane set at an angle \( \thet...

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A spool of thread of mass \( M \) is placed on an inclined smooth plane set at an angle \( \theta \) with the horizontal. The free end of the thread is attached to the wall as shown in the figure. The moment of inertia of spool about its axis is \( I \) and radius of wound thread layer is \( r \). Find the acceleration of centre of mass of the spool.
(a) \( \frac{g \sin \theta}{1+\frac{I}{M r^{2}}} \)
(b) \( \frac{g \sin \theta}{1+\frac{2 I}{M R^{2}}} \)
(c) \( \frac{2 g \sin \theta}{1+\frac{2 I}{M r^{2}}} \)
(d) \( \frac{2 g \sin \theta}{1+\frac{I}{M r^{2}}} \)
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