question_answer

A reel of thread unrolls itself falling under gravity. Neglecting mass of the thread, the acceleration of the reel is

A) \[g\]                                     

B) \[\frac{g}{2}\]

C) \[\frac{2g}{3}\]                                

D) \[\frac{4g}{3}\]

Correct Answer: A

Solution :

\[a=\frac{g}{\left( 1+\frac{{{k}^{2}}}{{{R}^{2}}} \right)}\] For solid cylinder\[\frac{{{K}^{2}}}{{{R}^{2}}}=\frac{1}{2}\] \[\therefore \]         \[a=\frac{g}{1+\frac{1}{2}}=\frac{2}{3}g\]