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An object of mass m is tied to a light string wound around a pulley that has a moment of inertia I and radius R. The axis of pulley is frictionless and the string does not slip on the pulley, then graph showing variation of $\frac{a}{g}$ versus $\frac{I}{m R^{2}}$ may be (Here a is acceleration of the object)

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Detailed Solution

$a = \frac{{mR}^{2}}{I + {mR}^{2}} g \Rightarrow \frac{a}{g} = \frac{1}{\frac{I}{{mR}^{2}} + 1} \frac{I}{{MR}^{2}} = 0$

$\frac{a}{g} = 1 if \frac{1}{{mR}^{2}} = \infty$

$\frac{a}{g} = \frac{1}{\infty + 1} = 0$

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