Solve the following :


The descending pulley shown in figure has a radius $20 \mathrm{~cm}$ and moment of inertia $0.20 \mathrm{~kg}^{-} \mathrm{m}^{2}$. The fixed pulley is light and the horizontal plane frictionless. Find the acceleration of the block if its mass is $1.0 \mathrm{~kg}$.


Translatory Motion Equation

$T_{1}=1, a-(\mathrm{i})$


Rotational Motion Equation

$\tau=\mathrm{I} \alpha$


$T_{2}-T_{1}=\frac{l}{R}\left(\frac{a}{2 R}\right)_{-(\mathrm{iii})}$

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


$\mathrm{m}=10 \mathrm{~kg}$-(iv)

Using, (i),(ii),(iii) and (iv)

$a=10 \mathrm{~m} / \mathrm{s}^{2}$

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