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A girl jumps from a height h on the end ...

A girl jumps from a height `h` on the end of a see-saw. The see-saw consists of a uniform plank of length `I` pivoted at its centre. The plank is horizontal before the girl jumps. The mass of the see-saw is twice the mass of the girl. Find the angular velocity of the plank just after the girl jumps on the plank.

Text Solution

Verified by Experts

When the girl lands on the plank, she exerts a force on it, similarly the plank exerts an equal and opposite force on the girl. For the system consisting of girl and plank these forces are internal, therefore angular mometum is conserved.
`vecL_(i)=1/2mlsqrt(2gh)`
`vecL_(f)=1/6ml^(2)omega+1/2ml^(2)omega`
`1/2mlsqrt(2gh)=5/12 ml^(2)omega`
`vecL_(f)=vecL_(f)impliesomega=6/5sqrt((2gh)/l)`
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