A string is wrapped on a wheel of moment of inertia $0.20 {kgm}^{2}$ and radius 10 cm and goes through a light pulley to support a block of mass 2.0 kg as shown in figure. Find the acceleration of the block. $(in m / s^{2}) g = 9.8 m / \sec^{2}$

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answer is 0.89.

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Detailed Solution

$\begin{array}{l} 2 g - T = 2 a . . . . (1) \\ a = R α . . . . (2) \\ T . R = I α . . . (3) \end{array}$
From (2) and (3)

$T = \frac{I a}{R^{2}}$
$∴ 2 g = a (2 + \frac{I}{R^{2}})$
$\Rightarrow a = \frac{2 g}{(2 + \frac{I}{R^{2}})} = \frac{2 \times 9.8}{2 + \frac{0.2}{0.01}} = \frac{9.8}{11} \approx 0.89 m / s^{2}$

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