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Question I have got 19.6 as the answer for (a) but the book tells 14 is the answer. Can someone tell what mistake I have done or is there in the book. This is my solution

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    $\begingroup$ hint the force in the rope is not mg. Why? Because the hanging mass is also accelerating. $\endgroup$
    – agentp
    Feb 6 '18 at 0:34
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You omitted the inertia of the mass of $0.5 kg$. The total inertia of the system is the inertia of the disk plus the inertia of the mass.

$$ I = \frac{M R^2}{2} + m R^2 $$

The total torque about the axle is $T= m g R$. Then use $I \alpha =T$ to get the equation

$$ \left(\frac{M R^2}{2} + m R^2\right)\alpha=m g R$$

This gives

$$\alpha=\frac{2 g m}{R (2 m+M)}=\frac{(2) (9.8) (0.5)}{(0.2)((2)(0.5)+2.5)}=\frac{9.8}{0.7}=14$$

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