Question 5

A mass $$m$$ is supported by a massless string wound around a uniform hollow cylinder of mass m and radius R. If the string does not slip on the cylinder, with what acceleration will the mass fall on release?

$$mg - T = ma \quad \text{--- (Equation 1)}$$

$$\tau = T \cdot R = I\alpha$$

$$I = mR^2$$

$$T \cdot R = (mR^2) \left(\frac{a}{R}\right)$$

$$T \cdot R = mR \cdot a$$

$$T = ma \quad \text{--- (Equation 2)}$$

$$mg - ma = ma$$

$$mg = 2ma$$

$$a = \frac{g}{2}$$

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