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A cylinder of mass \( M \) and radius \( r \) is mounted on a frictionless axle over a well. A rope of negligible mass is wrapped around the cylinder and a bucket of mass \( \mathrm{m} \) is suspended from the rope. The linear acceleration of the bucket will be-
(1) \( \frac{\mathrm{mg}}{\mathrm{M}+\mathrm{m}} \)
(2) \( \frac{\mathrm{mg}}{\mathrm{M}+2 \mathrm{~m}} \)
(3) \( \frac{2 m g}{M+2 m} \)
(4) \( \frac{\mathrm{M}}{\mathrm{mg}} \)
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