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

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

Punjab PMETPunjab PMET 2007

Solution:

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