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Question Number 109905 by ajfour last updated on 26/Aug/20

Answered by mr W last updated on 26/Aug/20

Commented by mr W last updated on 26/Aug/20

$$Mg\times \frac{L}{2}=\frac{1}{2}I{\omega }^2=\frac{1}{2}\times \frac{{ML}^2}{3}{\omega }_i^2$$$${\omega }_i=\sqrt{\frac{3g}{L}}$$$$e{\omega }_{i}L=v-{\omega }_{f}L$$$$\Rightarrow {\omega }_f=\frac{v}{L}-{\omega }_i=\frac{v}{L}-\sqrt{\frac{3g}{L}}$$$$\frac{{ML}^2}{3}{\omega }_i=\frac{{ML}^2}{3}{\omega }_f+mvL$$$${\omega }_i={\omega }_f+mv\times \frac{3}{ML}$$$$\sqrt{\frac{3g}{L}}=\frac{v}{L}-\sqrt{\frac{3g}{L}}+mv\times \frac{3}{ML}$$$$\Rightarrow v=\frac{2\sqrt{3gL}}{1+\frac{3m}{M}}$$$$x=vt=v\sqrt{\frac{2h}{g}}=\frac{2\sqrt{6Lh}}{1+\frac{3m}{M}}$$$$x=\frac{2\sqrt{6\times 1\times 0.5}}{1+\frac{3\times 0.1}{2}}=\frac{40\sqrt{3}}{23}=3.01m$$

Commented by ajfour last updated on 27/Aug/20

$$ThankyouSir,verynicesolution.$$

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