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## Homework Statement

## Homework Equations

## The Attempt at a Solution

I have solved the first part already.

For the 2nd part, I am writing the relevant eqns.

Can I take motion of the plank as a pure rotation about the pivot ?

Quantities corresponding to pivot is subscripted by p.

Conservation of momentum gives,

## mv_0 =mv_f + MV_f ## (1)

Conservation of Angular momentum about the pivot gives,

##2mv_0 l = 2mv_f l+ [ I_p \omega_p = I_{cen} \omega_{cen} + MV_f R] ~~~~~~(2)

\\ \omega_p = \omega_{cen} = V_f/l ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(3)

\\ mv_0 = mv_f + \frac { 2MV_f } 3 ~~~~~~~~~~~~~~~~~~~~(4) ## which contradicts eqn. (1)

Conservation of kinetic energy,

## \frac 1 2 m v_0^2 = \frac 1 2 m v_f^2 + [\frac 1 2 I_{p} ω^2 = \frac 1 2 I_{cen} ω^2 + \frac 1 2 M V_f^2] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(5)##

Are these equations correct?

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