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Question Number 216665 by Tawa11 last updated on 14/Feb/25

Commented by Tawa11 last updated on 14/Feb/25

In the figure, a cylinder of mass M, radius R and moment of inertia I = (MR²)/2 is placed on a horizontal table. The rope wound around the cylinder passes over an ideal massless pulley and is then tied to a block of mass, m = 2M. At the instant shown, the block is falling and the cylinder rolls without slipping, unwinding the rope. Find: a) the acceleration of the block, b) the acceleration of the center of mass of the spool

Answered by mr W last updated on 17/Feb/25

Commented by mr W last updated on 16/Feb/25

$$mA=mg-T$$$$\Rightarrow T=m(g-A)=2M(g-2a)$$$$(\frac{{MR}^2}{2}+{MR}^2)\frac{a}{R}=2RT$$$$\Rightarrow T=\frac{3Ma}{4}$$$$\frac{3Ma}{4}=2M(g-2a)$$$$19a=8g$$$$\Rightarrow a=\frac{8g}{19}✓$$$$\Rightarrow A=\frac{32g}{19}✓$$

Commented by Tawa11 last updated on 15/Feb/25

$$\mathrm{Thanks}\mathrm{sir}.$$$$\mathrm{I}\mathrm{appreciate}\mathrm{sir}.$$

Commented by mr W last updated on 15/Feb/25

$$answercorrect?$$

Commented by Tawa11 last updated on 16/Feb/25

$$\mathrm{No}\mathrm{answer}\mathrm{there}\mathrm{sir}.$$$$\mathrm{Just}\mathrm{question}\mathrm{sir}.$$

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