A man of mass M stands at one end of a plank of length L which lies at rest on a frictionless surface . The man of plank is M/3, the distance that the mass moves relative to the ground is
Since , external force on system is zero , so no change takes place in the centre of mass .
`x_(cm) = (m_1x_1 + m_2 x_2)/(m_1 + m_2)`
or ` Delta x_(cm) = (m_1 Delta x_1 + m_2 Delta x_2)/(m_1 + m_2)`
Here `Delta x_(cm) = 0`
`:.` `m_1 Delta x_1 + m_2 Delta x_2 = 0`
or ` M Delta x_1 + M/3 Delta x_2 = 0`
`:.` ` Delta x_1 = - (M)/(3M) Delta x_2 = - (Delta x_2)/(3)`........................(i)
But `x_(rel) = Delta x_1 - Delta x_2`
or `L= Delta x_1 - Delta x_2`
or ` L = - (Delta x_2)/(3) - Delta x_2 = - 4/3 Delta x_2` [from eq.(i)
`because Delta x_2 = - 3/4 L`
`:.` `Delta x_1 = - (Delta x_2)/(3) = - (-3L)/(4 xx 3) = - L/4`
Negative sign indicates that both moves in opposite directions.
Submit Your Solution hear: