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Question
A Merry-go-round, made of a ring-like platform of radius R and mass M, is revolving with angular speed ω. A person of mass M is standing on it. At one instant, the person jumps off the round, radially away from the centre of the round (as seen from the round). The speed of the round afterwards is ______.
Options
2ω
ω
`ω/2`
0
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Solution
A Merry-go-round, made of a ring-like platform of radius R and mass M, is revolving with angular speed ω. A person of mass M is standing on it. At one instant, the person jumps off the round, radially away from the centre of the round (as seen from the round). The speed of the round afterwards is 2ω.
Explanation:
`I_1ω_1 = I_2ω_2`
`m_1 = 2M`
`m_2 = M`
`ω_1 = ω`
`ω_2` = ?
`r_1 = R`
`r_2 = R`
When a person leaps down tangentially, i.e. from the perimeter,
∴ `m_1r_1^2ω_1 = m_2r_2^2ω_2`
`2MR^2ω = MR^2ω_2`
`ω_2 = 2ω`
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